A continuously variable valve timing apparatus may include a camshaft, a plurality of wheels mounted to the camshaft, of which a wheel key is formed thereto respectively, a plurality of cam portions of which a cam and a cam key are formed thereto respectively, of which the camshaft is inserted thereto, of which relative phase angle with respect to the camshaft is variable, a plurality of inner brackets connected with the each wheel key and the each cam key, a plurality of a slider housings of which the each inner bracket is rotatably inserted thereto respectively, and rotatably configured around a hinge hole formed an upper side of a cam cap and a control portion selectively moving the slider housings to change relative position of a rotation center of the inner brackets.