A multi-anode microchannel plate photomultiplier (Ma MCP-PMT) is an appropriate photo sensor for particle identification in high energy physics experiments such as PANDA, Belle II, etc. Since these detectors usually work in a strong magnetic field, the sensors must be immune to the field. In this article, the effects of the magnetic field on the conventional MCP and the atomic layer deposited MCP (ALD-MCP) are studied by simulating the electron multiplication in the microchannel of the MCP. Simulation results show that the gain of conventional MCP-PMTs increases a little before it starts decreasing while the magnetic field is further increasing. We found that the shortening of electronic trajectories and the reduction of secondary electrons mainly contribute to gain variations of a conventional MCP. For the ALD-MCP that usually has higher secondary emission yields, it is found that high re-diffusion secondary electron yields could make it more vulnerable to magnetic fields.