A continuous variable valve duration apparatus may include a camshaft, a cam unit 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 inner bracket transmitting rotation of the camshaft to the cam unit, a wheel housing in which the inner bracket is rotatably inserted, on which a guide groove parallel to the camshaft is formed, and on which a guide hole vertical to the camshaft is formed, a guide portion including a guide shaft inserted into the guide hole for guiding movement of the wheel housing and 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.