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