A continuous variable valve duration apparatus may include: a camshaft; a cam unit on which a cam is formed, and the camshaft inserted to the cam; an inner wheel for transmitting rotation of the camshaft to the cam unit; a wheel housing into which the inner wheel is rotatably inserted and movable perpendicular to the camshaft; a guide shaft on which a guide screw thread is formed and disposed perpendicular to the camshaft; a worm wheel formed with an inner screw thread for engaging with the guide screw thread, and the worm wheel disposed within the wheel housing; and a control shaft on which a control worm for engaging with the worm wheel is formed.