In order to optimize accuracy and complexity of SINS algorithm, this work applied Fourth-order Runge-Kutta algorithm on attitude and velocity calculation. It is shown that this method leads to a better performance. First of all, high accuracy digital integration algorithm for calculating attitude, velocity and position was carried out according to the previous findings was introduced. After that, new algorithms of attitude and velocity calculation using the theory of Runge-Kutta algorithm were deduced in detail. By adopting the data of trajectory generator, the error feature curves of navigation results from the two algorithms (that is the previous digital integration algorithm and the new algorithm based on Runge -Kutta algorithm) were obtained, respectively. Comparison with the two algorithms clearly shows that the performance of Fourth-order Runge-Kutta algorithm is better than that of high accuracy digital integration algorithm.