I want to copy datagridview data to dataset without using a database.

Couldn't guess out why you need a class to do the same! Still, here it is...

You can get like this:

//If DataSource of GridView1 is a DataTable
DataTable dt = (DataTable)GridView1.DataSource;
//Now add this table to DataSet

If you want to make some changes while porting the data, you have to loop through. You have to manually create columns first, then loop through all the rows.

//This is just a Psuedocode
DataTable dt = new DataTable();
//Add columns here
dt.Columns.Add(); //or something similar
//go on till all the columns are added
//loop and second loop
foreach(GridViewRow gvr in GridView1.Rows)
{
   DataRow dr = dt.NewRow();
   
   //second loop - looping all columns
   for(int i = 0; i < gvr.Rows.Count; ++i)
   {
      dr[i] = gvr.Cells[i].Text;
   }
}
//Add datatable to Dataset as you want here

Now if you want, you can put this piece of code in a class and expose it. Call it when you need to.