This paper proposes an accelerated testing method for automated vehicles safety evaluation based on improved importance sampling (IS) techniques. Taking the typical cut-in scenario as example, the proposed method extracts the critical variables of the scenario. Then, the distributions of critical variables are statistically fitted. The genetic algorithm is used to calculate the optimal IS parameters by solving an optimization problem. Considering the error of distribution fitting, the result is modified so that it can accurately reveal the safety benefits of automated vehicles in the real world.