Modern video coding standards have high coding efficiency, but the encoding performance has to be improved to meet the growing multimedia applications. The paper deals with the entropy encoding methods and algorithms in video coding standard H.264/AVC and H.265/HEVC. Context-based Adaptive Variable Length Coding (CAVLC) for the H.264/AVC standard was originally designed for lossy video coding, and as such does not yield adequate performance for lossless video coding. Context-Adaptive Binary Arithmetic Coding (CABAC) is a method of entropy coding first introduced in H.264/AVC and now used in the standard H.265/HEVC. While it provides high coding efficiency, the data dependencies in H.264/AVC CABAC make it challenging to parallelize and thus, limit its throughput. Accordingly, during the standardization of entropy coding for HEVC, both coding efficiency and throughput were considered. Based on an analysis of their advantages and disadvantages, a method called the entropy coding algorithm using the enumerative coding of the hierarchical approach is proposed. The proposed algorithm consists of the Context-Adaptive Binary Arithmetic Coding algorithm and the enumerative coding algorithm with a hierarchical approach. The proposed algorithm is tested in the Visual C ++ development environment on various test video sequences. The results of the experiments showed a greater efficiency of coding of multimedia data (the proposed one reduces on average up to 15% of the storage volume compared to the traditional CABAC method), while the method requires a longer coding time (approximately twice). The proposed method can be recommended for use in telecommunication systems for storage, transmission and processing of multimedia data, where a high degree of compression is required first.