A continuously variable valve duration apparatus may include a camshaft, a cam unit on which a cam is formed, wherein the camshaft is inserted into the cam unit, first and second guide brackets into which the camshaft is inserted, a wheel housing movably mounted to the first guide bracket and the second guide bracket, respectively, an internal wheel rotatably provided on each wheel housing and transmitting rotation of the camshaft to the cam unit, a worm wheel mounted on the first guide bracket and the second guide bracket, respectively to engage the wheel housing, a control shaft which is rotatably mounted on the first guide bracket and the second guide bracket, and engages with the each worm wheel to move the position of the wheel housing according to its rotation, and a connecting member that connects the first guide bracket and the second guide bracket.