We know that electricity is the flow of electrons.Am i right? Protons do not move. Then why is the conventional current defined as the direction in which the positive charges would move?

Electricity was discovered much before electrons and protons were discovered. IT was thought that positive charges are flowing and the direction was given. When later electrons were discovered and their conduction, a convention had established. So, it was thought that let the ‘convention‘ remain the same as it would cause people all over the world to change their used direction.