A continuously variable valve duration apparatus includes a camshaft, a cam unit on which a cam is formed, a guide bracket including an upper guide boss, an internal wheel configured to transmit rotation of the camshaft to the cam unit, a wheel housing in which the internal wheel is rotatably inserted, wherein a guide thread is formed in a portion of the wheel housing, and of which a guide shaft is formed to be movably inserted into the upper guide boss, a worm wheel to which an internal thread engaging with the guide thread is formed in the worm wheel, and to which an external thread is formed thereon, a control shaft on which a control worm engaged with the external thread is formed, and an upper bushing mounted on a lower portion of the upper guide boss to support the guide shaft.