Hi,
Please try below code.Change code as per your table structure(i.e. parent-child relationship),as we know we need to delete child table record first and then parent table record.
C#
try
{
    using (NWindDataContext dc = new NWindDataContext())
    {
        var q =
            (from c in dc.GetTable<Customer>()
            where c.CustomerID == "AAAAA"
        select c).Single<Customer>();
        foreach (Order ord in q.Orders)
        {
            dc.GetTable<Order>().DeleteOnSubmit(ord);
            foreach (Order_Detail od in ord.Order_Details)
            {
                dc.GetTable<Order_Detail>().DeleteOnSubmit(od);
            }
        }
        dc.GetTable<Customer>().DeleteOnSubmit(q);
        dc.SubmitChanges();
    }
    UpdateDataGrid();
}
catch (Exception ex)
{
   Response.Write(ex.Message);
}
VB
Try
	Using dc As New NWindDataContext()
		Dim q = (From c In dc.GetTable(Of Customer)() Where c.CustomerID = "AAAAA"c).[Single](Of Customer)()
		For Each ord As Order In q.Orders
			dc.GetTable(Of Order)().DeleteOnSubmit(ord)
			For Each od As Order_Detail In ord.Order_Details
				dc.GetTable(Of Order_Detail)().DeleteOnSubmit(od)
			Next
		Next
		dc.GetTable(Of Customer)().DeleteOnSubmit(q)
		dc.SubmitChanges()
	End Using
	UpdateDataGrid()
Catch ex As Exception
	Response.Write(ex.Message)
End Try
I hope this will help you out.