This paper analyzes the convergence rate of sample matrix inversion (SMI) filter used by array receivers in pulse interference environment. Firstly, the convergence characteristics of SMI filter under pulse interference are deduced, and the relationship between the convergence speed and length of training samples and duty of interference is given. Then, the results of signal simulation are consistent with those of numerical analysis, which verifies the correctness of theoretical analysis. The results show that the convergence speed of SMI filter decreases under pulse interference, and the SMI filter needs more training samples to suppress the pulse interference effectively.