A continuous variable valve duration apparatus may include a cam rotatably mounted on a cam carrier, a camshaft disposed within the cam and relatively rotatable with respect to the cam, in which a rotation center of the camshaft is variable with respect to a rotation center of the cam, a connecting link disposed between the cam and the camshaft, in which the connecting link is pivotally connected to at least one of the cam and the camshaft, and transmits rotation of the camshaft to the cam, and a control portion selectively changing the rotation center of the camshaft.