An apparatus of controlling a pulley of a continuously variable transmission and a method therefore is provided. The apparatus includes a non-transitory storage configured for storing a deep learning model, learning of which is completed and a controller that predicts a vehicle speed and an accelerator position sensor (APS) value for each future time point based on the deep learning model and controls the pulley of the continuously variable transmission based on a pulley ratio for each future time point, the pulley ratio corresponding to the predicted vehicle speed and the predicted APS value, thus preventing a reverse control phenomenon of the pulley ratio and increasing a tension of the belt in the continuously variable transmission.