An apparatus and a method for video encoding/decoding using predictability of an intra-prediction mode are disclosed. The apparatus for encoding a video of the present disclosure includes: an intra-prediction mode determiner for determining an encoder prediction mode which is an intra-prediction mode of a current block of the video; an encoder for encoding a residual block generated by subtracting, from the current block, a predicted block generated by predicting the current block according to the encoder prediction mode; a mode information generator for generating mode information according to whether or not a video decoding apparatus is able to predict the encoder prediction mode; and an encoded data generator for generating encoded data including the encoded residual block and the mode information. The present disclosure can enhance compression in video encoding/decoding by using intra-prediction to predict the video with a minimum necessary bit rate.