Owing to the severe loss of photoelectrons striking at the input electrode of conventional microchannel plate (MCP), photoelectron collection efficiency (CE) of devices based on traditional MCP fluctuates around the MCP open area ratio and cannot make a breakthrough. Photoelectron back scattering from the MCP surface also causes late pulses smearing timing and spatial performance. In this work, a novel bowl-shaped MCP with an open area ratio higher than 90% whose input electrode is coated by a thin film with high secondary electron emission yield (SEY) is proposed as an effective approach to improve CE and suppress late pulses. A three-dimensional MCP-PMT model is developed in CST Studio Suite to evaluate CE and time performance of the bowl-shaped MCP, and compared with the traditional one. Results show that CE of the PMT based on the bowl-shaped MCP is nearly 100% and the delayed pulse is less than 2%. This indicates that good temporal and spatial resolution can be achieved with the bowl-shaped MCP.