Proton exchange membrane water electrolyzer (PEMWE) is a promising technology to consume the fluctuating renewable energy and generate green hydrogen. However, the dynamic responses of physical parameters are still unclear during the fluctuating operation. Herein, a three-dimensional multi-physics model including mass and heat transfer, fluid flow, hydrogen crossover and electrochemical reactions is developed. The transient simulations are conducted and responses of critical parameters towards the fluctuation are analyzed. The temperature response shows a delay of ∼15 s to reach the steady state, and the overshoot phenomena are observed for the oxygen concentration and voltage when the current density is suddenly changed. Hydrogen crossover shows a sharp rise when the current density is decreased abruptly. The peak value of anode H2 in O2 vol% is twice the steady-state value when the current density decreases to 0.1 A cm−2. This work provides a comprehensive understanding of parameter behaviors under fluctuating conditions and guides the design of specific components.