In the space gravitational wave detection Taiji mission, a heterodyne laser interferometer is used to detect gravitational wave signals in the middle and low frequency bands. In the Taiji mission, the laser interferometry system is composed of multi-channel interferometers, which involves the phase acquisition and readout of multiple sets of the interference signals. Therefore, the multi-channel phase measurement system is one of the key core technologies of the space laser interferometry. In this paper, a multi-channel phase measurement system is proposed, designed and tested based on the requirements of the Taiji mission and its ground-based laser interferometry experiments. First, the hardware and software design of the multi-channel phase measurement system is given, including hardware architecture design, phase measurement algorithm based on digital phase-locked loop and its implementation on FPGA, software architecture design, etc. Second, a time-domain functional tests of the multi-channel phasemeter are performed, which includes the phase accuracy and linearity. The results show that the dynamic and static phase linearity and accuracy of the multi-channel phase measurement system under different working conditions are good. Finally, the frequency domain noise tests of different channels at different frequencies and different amplitudes are carried out. The results show that the phase noise level of the multi-channel phase meter designed in this paper is better than $ 2{\text{π}} {\text{µ}} {\rm{rad}}/\sqrt{{\rm{Hz}}} $ in the frequency band of 0.1 mHz-1 Hz. There is good consistency between different channels, and the phase noise introduced by channel differences or ADC chip differences is negligible in the target frequency band. For any interference signal with a frequency between 5-25 MHz, the phasemeter can meet the requirements within the target frequency band. Therefore, the multi-channel phase measurement system meets the requirements of space gravitational wave detection and ground-based interference experiments. At the same time, the research results of this paper also provide an experimental basis for expanding the phase measurement system with more channels in the future.