A rotation support mechanism and a portable terminal having a rotation support function that allows a cover to semi-automatically open from a closed position to an open position in a horizontal or a vertical position, enabling a user to open the cover to a desired open position by one hand and one-touch operation. The rotation support mechanism allows the cover to rotate from the closed position at which a vertically long body and the cover are closed in a superposed manner to the open position at which the cover is stopped after it is rotated by a certain angle in a plane in which the body and the cover are superposed on each other. The rotation of the cover integral with an eccentric cam can be stopped at rotation positions of multiple stages in the horizontal or the vertical position by a pressing means that presses, in the plane, the cam surface of the eccentric cam.