Depositing a high secondary electron yield (SEY) film on the microchannel plate (MCP) input electrode is supposed to be an effective approach to improve the photoelectron collection efficiency (CE) of photomultiplier tubes based on MCPs (MCP-PMTs). Nevertheless, secondaries promoted by the photoelectrons striking the MCP input face may cause a long tail in the time distribution of the output electrons (TDOE). In our work, laying a conductive grid upon the MCPs is proposed as an effective approach to suppress the tail. A three-dimensional MCP-PMT model is developed in CST STUDIO SUITE to systematically investigate the dependence of the TDOE on the applied voltage (U) of the grid at the coated material SEY=6. Simulation results show that high voltage applied on the grid could suppress the delay pulse effectively. The optimal U is above 500 V. © 2019 SPIE.