In this paper, we present a novel impatience model where impatience level dynamically changes with time. Quantitative formulas are introduced to calculate the dynamic impatience level considering both self-growth and the impatience propagation. Unlike conventional methods using either random updated sequence or fixed sequence. At each time step, all the pedestrians will move to the target cell depending on the impatience level. The dynamic impatience model is implemented in Cellular Automata model where space and time are discretized to simulate the crowd evacuation process. Numerical simulations are conducted to demonstrate the feasibility of this model. The simulation results show that this model can successfully reproduce typical collective behavior (e.g., clogging phenomenon). We also performed parameter sensitivity study of the dynamics growth and the propagation speed. Results show that with the increase of propagation speed, the evacuation efficiency is initially promoted sharply and the efficiency begins to decline. Another finding is the psychological impatience is not always negative to the moving efficiency. At low impatience value, the increase of the impatience level can improve the evacuation efficiency, while at higher impatience value, the evacuation efficiency drops continuously with the increase of impatience level. These findings will be helpful to control pedestrian emotion (e.g.,impatience level) effectively.