Measurement of the angular velocity of flight vehicles is one of the most important problem in the aerospace field. However, the gyroscope, as the dominating measuring device for the angular velocity measurement, is expensive. In this paper, a method for obtaining the angular velocity of the rigid body is proposed, based on measuring the accelerations of three non-collinear points. The angular velocity is calculated by using the base-point method in mechanics of rigid bodies, and the errors of the angular velocity are also analyzed. In order to validate the new model, a numerical simulation is carried out to analyze the applicability of this method for a spacecraft in the high angular velocity situation or for a satellite in the low angular velocity situation. The result indicates that this method can be applied for the spacecraft with a high angular velocity and in a steady state.