how to add the checkbox to the datagridview from coding

I think the easiest way to add Checkbox column in datagrid view is from the UI

              Step1 : Select the dataGrid at the UI
              Step2: Select Edit Column
              Step3: Click on the column name in edit Columns Window
              Step4:Select column type = "DataGridViewCheckBoxColumn"
              Step5: click ok

Attached a snaphot

For these kind of questions you can just add the control through the designer and see what Visual Studio did in the code behind file.

Assuming that you mean how to add a checkbox column to a DataGridView dynamically:

DataGridViewCheckBoxColumn col = new DataGridViewCheckBoxColumn();
... // set properties as needed here
dataGridView1.Columns.Add(col);

If you meant to add a column with checkboxes:

DataGridViewCheckBoxColumn checkColumn = new DataGridViewCheckBoxColumn();
checkColumn.Name = "X";
checkColumn.HeaderText = "X";
checkColumn.Width = 50;
checkColumn.ReadOnly = false;
checkColumn.FillWeight = 10; //if the datagridview is resized (on form resize) the checkbox won't take up too much; value is relative to the other columns' fill values
dataGridView1.Columns.Add(checkColumn);