如果移动for循环，则无需建立多个连接。只需对您的代码块进行快速编辑（绝对不完全正确）：

If you move your for loop, you won't have to make multiple connections. Just a quick edit to your code block (by no means completely correct):

string StrQuery;
try
{
    using (SqlConnection conn = new SqlConnection(ConnString))
    {
        using (SqlCommand comm = new SqlCommand())
        {
            comm.Connection = conn;
            conn.Open();
            for(int i=0; i< dataGridView1.Rows.Count;i++)
            {
                StrQuery= @"INSERT INTO tableName VALUES (" 
                    + dataGridView1.Rows[i].Cells["ColumnName"].Text+", " 
                    + dataGridView1.Rows[i].Cells["ColumnName"].Text+");";
                comm.CommandText = StrQuery;
                comm.ExecuteNonQuery();
            }
        }
    }
}

要一次执行多个SQL命令，请查看以下链接：
单个语句中有多个语句SqlCommand

As to executing multiple SQL commands at once, please look at this link: Multiple statements in single SqlCommand