A variable valve lift apparatus to vary lift of a valve disposed at an engine may include an outer body selectively making a lever motion according to rotation of a cam, being adapted such that the valve is connected with one end thereof and a pivot axis of the lever motion is disposed at another end thereof, and forming an inside space, an inner body disposed in the inside space of the outer body and adapted such that one end thereof is rotatably connected with the one end of the outer body, a connecting shaft disposed so as to penetrate the one end of the outer body and the one end of the inner body and connect the outer body with the inner body, and a lost motion spring provided so as to return the inner body which is relatively rotated with the outer body around the connecting shaft.