Micro-channel plate photomultiplier tube (MCP-PMT) is a kind of photosensitive device with single photon detection capability and great time resolution, which is also called Fast-PMT (FPMT). The MCP is the electron multiplier structure and in order to achieve single photon detection, two layers of MCPs are always used together. Due to the new-generation particle accelerators with high energy and luminosity, the time resolution of the detector is more important than single-photon detection capability. The single-chip-FPMT is expected to have a greater time resolution. Based on the CST STUDIO SUITE, the single-chip-FPMT model is built and the time performances including the rise time and transit time spread are compared with the double-chips-FPMT model under the same parameter setting. The results show that the FPMT model with single chip MCP has better time response and resolution than the traditional double-chips-FPMT.