This paper introduces an attitude updating method based on a new structure of gyroscope-free inertial navigation system(GFINS), in which the angular accelerometers are used to take the place of gyroscopes. For this new structure of GFINS, a new mathematical model is developed to determine the general three-dimensional motion of body segments. The mathematical model is mainly based on the direction cosine matrix. A second-order differential equation which is represented by angular acceleration should be calculated to solve this problem using the fourth order Runge-Kutta method combining with the interpolation method. Furthermore, the final result of this approach is shown by applying the mathematical model to some simulation data generated by the trajectory generator. The simulation results indicate that the mathematical model has a good performance.