The power-inversion adaptive array is very suitable for situations where the desired signals are very weak while the interfering signals are much stronger, thus, it is widely used in the global navigation satellite system. For least mean square based on power-inversion adaptive array which is used in global navigation satellite system receivers, the convergence rate was very slow when sudden change in interference number or interference power occurs. The performance of receiving the satellite signals would be degraded. The cause of this phenomenon was analyzed. Then, an improved least mean square algorithm was proposed to solve this problem. The key novelty of the proposed method was that it monitors the power of the reference antenna output to detect any sudden change in interference number or interference power. Once the interference number or interference power decreases suddenly, the weight vector would be initialized again to improve the rate of convergence. Simulation results show that the improved method outperforms the original algorithm in rate of convergence.