In this paper, we propose a spatial mode demultiplexing technique that uses a volume holographic demultiplexer (VHDM) with a phase plate. The VHDM can separate the multiplexed spatial modes with a single device by using angularly multiplexed volume holograms. In the VHDM, modal cross-talks, which are called inter-page cross-talks in the holographic data storages, are generated, and hence the separation performance of the VHDM is degraded by the intensity overlap between spatial modes. Therefore, we propose a novel scheme wherein phase modulation with a phase plate is added to the conventional scheme. The proposed scheme can achieve high separation performance by modulating the phase of spatial modes to reduce the intensity overlap. In this study, we demonstrated the basic operation of the proposed method for a specific linearly polarized mode group. The separation performance of the VHDM was observed to be markedly improved by the proposed method.