Cold start is one of the urgent problems to be solved in the process of commercialization for the polymer electrolyte membrane fuel cell (PEMFC). In this study, cold start processes under constant power start‐up are simulated with a three‐dimensional transient model. Evolutions of voltage and current density under higher and lower current density under this mode are elucidated. The water accumulation location in the PEMFC is analyzed and effects of important parameters on the process of cold start are quantified under constant power start‐up mode. The results show that the current density first increases and then decreases when the PEMFC starts from a higher current density under constant power start‐up mode, while it is reversed when the PEMFC starts from a lower current density. Ice first appears in the area near the membrane under the channel and the hottest area in the cell also appears below the channel. At the lower current density, the distribution of water in ionomer is more uniform. Under two different starting current densities, the changing trends of the conductivity of the membrane and the anode catalyst layer are different. The activational heat is the largest heat source in the cold start process under constant power start‐up mode and the utilization of ionomer water storage is higher when the PEMFC starts from a lower current density. The temperature of the inlet gas is most sensitive to the cold start process at lower current density. And initial content of membrane water and membrane thickness have important impacts on the cold start performance when PEMFC starts from a higher current density due to the redistribution of potential.