In this article I am posting code about swapping GridView rows Up and Down using Data Tables.
Here is Aspx Code

<form id="form1" runat="server">
 <div>
 <asp:Label ID="Label1" runat="server" ForeColor="red" Text="Label"></asp:Label>
 <br />
 <br />
 <asp:GridView ID="Gridviewselectbus" runat="server" Height="87px" Width="771px"
 HorizontalAlign="Center" AutoGenerateColumns="False" OnRowCommand="Gridviewselectbus_RowCommand" CellPadding="4" ForeColor="#333333" GridLines="None">
 <RowStyle BorderColor="#999999" HorizontalAlign="Center" VerticalAlign="Middle"
 Wrap="True" BackColor="#EFF3FB" />
 <EmptyDataRowStyle BorderColor="#999999" />
 <Columns>
 <asp:BoundField DataField="Lname" HeaderText="Lname" SortExpression="Lname" />
 <asp:BoundField DataField="Fname" HeaderText="Fname" SortExpression="Fname" />
 <asp:BoundField DataField="Job" HeaderText="Job" SortExpression="Job" />
 <asp:BoundField DataField="Index" HeaderText="Index" SortExpression="Index" />
 <asp:TemplateField>
 <HeaderStyle Width="3%" />
 <ItemTemplate>
 <asp:ImageButton ID="ibtnUp" runat="server" border="0" CommandArgument='<%# Eval("index")%>'
 CommandName="Up" Height="18px" ImageUrl="images/btn_GreenUP.png" Width="18px" />
 </ItemTemplate>
 </asp:TemplateField>
 <asp:TemplateField>
 <HeaderStyle Width="3%" />
 <ItemTemplate>
 <asp:ImageButton ID="ibtnDown" runat="server" border="0" CommandArgument='<%# Eval("index")%>'
 CommandName="Down" Height="18px" ImageUrl="images/btn_GreenDown.png" Width="18px" />
 </ItemTemplate>
 </asp:TemplateField>
 </Columns>
 <FooterStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
 <PagerStyle BackColor="#2461BF" ForeColor="White" HorizontalAlign="Center" />
 <SelectedRowStyle BackColor="#D1DDF1" Font-Bold="True" ForeColor="#333333" />
 <HeaderStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
 <EditRowStyle BackColor="#2461BF" />
 <AlternatingRowStyle BackColor="White" />
 </asp:GridView>
 </div>
 </form>
Here is C# code

public partial class _Default : System.Web.UI.Page
{
 public DataTable dt = new DataTable();
 public DataTable dtnew = new DataTable();

 protected void Page_Load(object sender, EventArgs e)
 {
 if (!IsPostBack)
 {
 bindgrid(); // Bind Gridview with sample data
 }
 }

 private void bindgrid()
 {
 dt.Columns.Add("Fname");
 dt.Columns.Add("Lname");
 dt.Columns.Add("Job");
 dt.Columns.Add("Index");
 DataRow dr;
 dr = dt.NewRow();
 dr[0] = "ONE";
 dr[1] = "User One";
 dr[2] = "Manager";
 dr[3] = 0;
 dt.Rows.Add(dr);
 dr = dt.NewRow();
 dr[0] = "TWO";
 dr[1] = "User Two";
 dr[2] = "Project Lead";
 dr[3] = 1;
 dt.Rows.Add(dr);
 dr = dt.NewRow();
 dr[0] = "THREE";
 dr[1] = "USer Three";
 dr[2] = "Team Lead";
 dr[3] = 2;
 dt.Rows.Add(dr);
 dr = dt.NewRow();
 dr[0] = "FOUR";
 dr[1] = "User Four";
 dr[2] = "Module Lead";
 dr[3] = 3;
 dt.Rows.Add(dr);
 dr = dt.NewRow();
 dr[0] = "FIVE";
 dr[1] = "User Five";
 dr[2] = "Senior Developer";
 dr[3] = 4;
 dt.Rows.Add(dr);
 dr = dt.NewRow();
 dr[0] = "SIX";
 dr[1] = "User Six";
 dr[2] = "Developer";
 dr[3] = 5;
 dt.Rows.Add(dr);
 dt.AcceptChanges();
 Gridviewselectbus.DataSource = dt;
 Gridviewselectbus.DataBind();
 Session["dt"] = dt;
 }

protected void Gridviewselectbus_RowCommand(object sender, GridViewCommandEventArgs e)
 {
 if (e.CommandName == "Up")
 {
 int index = Convert.ToInt32(e.CommandArgument);
 if (index == 0)
 {
 Label1.Text = "You Cant move recor' Up";
 Label1.Visible = true;
 return;
 }
 dt = (DataTable)Session["dt"];
 int value = Convert.ToInt32(dt.Rows[index]["Index"].ToString());
 dt.Rows[index]["Index"] = Convert.ToInt32(index) - 1;
 dt.Rows[index - 1]["Index"] = value;// Convert.ToInt32(index);
 dt.DefaultView.Sort = "Index";
 dt.AcceptChanges();
 dtnew = dt.Copy();
 Gridviewselectbus.DataSource = dt;
 Gridviewselectbus.DataBind();
 dt.AcceptChanges();
 for (int i = 0; i <= Gridviewselectbus.Rows.Count - 1; i++)
 {
 dtnew.Rows[i]["Lname"] = Gridviewselectbus.Rows[i].Cells[0].Text;
 dtnew.Rows[i]["Job"] = Gridviewselectbus.Rows[i].Cells[1].Text;
 dtnew.Rows[i]["Fname"] = Gridviewselectbus.Rows[i].Cells[2].Text;
 dtnew.Rows[i]["Index"] = Gridviewselectbus.Rows[i].Cells[3].Text;
 }
 Session["dt"] = dtnew;
 Label1.Text = string.Empty;
 }
 if (e.CommandName == "Down")
 {
 int index = Convert.ToInt32(e.CommandArgument);
 dt = (DataTable)Session["dt"];
 if (Convert.ToInt16(index + 1) == dt.Rows.Count)
 {
 Label1.Text = "You Cant move record down";
 Label1.Visible = true;
 return;
 }
 int value = Convert.ToInt32(dt.Rows[index]["Index"].ToString());
 dt.Rows[index]["Index"] = Convert.ToInt32(dt.Rows[index]["Index"].ToString()) + 1;
 dt.Rows[index + 1]["Index"] = value;
 dt.AcceptChanges();
 dt.DefaultView.Sort = "Index";
 dt.AcceptChanges();
 dtnew = dt.Copy();
 Gridviewselectbus.DataSource = dt;
 Gridviewselectbus.DataBind();
 dt.AcceptChanges();
 for (int i = 0; i <= Gridviewselectbus.Rows.Count - 1; i++)
 {
 dtnew.Rows[i]["Lname"] = Gridviewselectbus.Rows[i].Cells[0].Text;
 dtnew.Rows[i]["Job"] = Gridviewselectbus.Rows[i].Cells[1].Text;
 dtnew.Rows[i]["Fname"] = Gridviewselectbus.Rows[i].Cells[2].Text;
 dtnew.Rows[i]["Index"] = Gridviewselectbus.Rows[i].Cells[3].Text;
 }
 Session["dt"] = dtnew;
 Label1.Text = string.Empty;
 }
 }
}
Thanks :)