As a dynamic error of fiber optic gyroscope (FOG), angular acceleration error will induce attitude error into FOG strap down inertial navigation system and constrain the performance of the system under severe angular motion. Based on the dynamic model of closed loop FOG, angular acceleration error model is setup and its determined factors (including the total gain and period of the control loop of the FOG) are analyzed. Correspondingly, the angular acceleration error decrease method is proposed. In order to exam this model, the angular acceleration error of the closed loop is tested by applying a slope signal to the feedback step wave of the FOG, based on the equivalent input principal. And the test result under different angular acceleration and total gain of different control loop is in accord with the model.