With the capability of achieving twice the compression ratio of Advanced Video Coding (AVC) with similar reconstruction quality, High Efficiency Video Coding (HEVC) is expected to become the newleading technique of video coding. In order to reduce the storage and transmission burden of digital holograms, in this paper we propose to use HEVC for compressing the phase-shifting digital hologram sequences (PSDHS). By simulating phase-shifting digital holography (PSDH) interferometry, interference patterns between illuminated three dimensional (3D) virtual objects and the stepwise phase changed reference wave are generated as digital holograms. The hologram sequences are obtained by the movement of the virtual objects and compressed by AVC and HEVC. The experimental results show that AVC and HEVC are efficient to compress PSDHS, with HEVC giving better performance. Good compression rate and reconstruction quality can be obtained with bitrate above 15000kbps.