A continuously variable valve timing apparatus may include a camshaft, a first and a second cam portions having two cams formed thereto, of which the camshaft is inserted thereinto, and of which relative phase angles with respect to the camshaft are variable. First and second inner brackets transmit rotation of the camshaft to the first and second cam portions respectively. First and second slider housings having first and second inner brackets are rotatably inserted thereinto, respectively, and have relative positions with respect to the camshaft that are variable. A cam cap rotatably supports the first and second cam portions together with a cylinder head, and the slider housings are slidably mounted thereto. A control shaft is disposed parallel with the camshaft and selectively moves the first and the second slider housings, and a control portion selectively rotates the control shaft so as to change positions of the inner brackets.