A continuous variable valve duration apparatus may include: a camshaft; first and second cam portions on which a cam is formed respectively, the camshaft inserted to the first and second cam portions of which relative phase angles with respect to the camshaft are variable; first and second inner brackets transmitting rotation of the camshaft to the first and second cam portions respectively; a cam lifter in which the first and second inner brackets are rotatably inserted, and a cam lifter guide slantly formed on the cam lifter; a cam cap rotatably supporting the first and the second cam portions, and the cam lifter slidably mounted to the cam cap; a control portion including a screw shaft parallel to the camshaft; and an adapter engaged with the screw shaft, on which an adapter guide slidably engaged with the cam lifter guide and moving a relative position of the cam lifter.