A continuous variable valve duration apparatus may include a camshaft, a cam device on which a cam is formed, of which the camshaft is inserted thereto and of which a relative phase angle with respect to the camshaft is variable, an internal bracket transmitting rotation of the camshaft to the cam device, a wheel housing in which the internal bracket is rotatably inserted and on which a guide groove parallel to the camshaft is formed, a control portion including a control shaft disposed parallel to the camshaft and inserted into the guide groove, and the control portion selectively rotating the control shaft for the relative position of the wheel housing with respect to the camshaft to be changed and a slider housing interposed between the control shaft and the guide groove.