Don't do it like that. OK, you are replacing quote with a pair of quotes, but that doesn't really protect you well - and makes your code very difficult to read.
Instead, use parameterised queries:
Using con As New MySqlConnection(strConnect)
con.Open()
Using com As New MySqlCommand("INSERT INTO myTable (myColumn1, myColumn2) VALUES (@C1, @C2)", con)
com.Parameters.AddWithValue("@C1", myValueForColumn1)
com.Parameters.AddWithValue("@C2", myValueForColumn2)
com.ExecuteNonQuery()
End Using
End Using
It's safer, you don't need to faff with Replace, and it's a whole load more readable. You'll probably find that it fixes your problem at the same time.