The failure probability-based moment-independent sensitivity index well analyzes how uncertainty in the failure probability of a model can be apportioned to different sources of uncertainty in the model inputs. At present, the existing sampling-based methods to estimate this index can not make full use of samples. Therefore, in this paper, we mainly concern how to improve the utilization of samples to accurately estimate this index. Based on the law of total variance in the successive intervals without overlapping proved in this paper, we propose an efficient method to estimate the failure probability-based moment-independent sensitivity index by combining the idea of space-partition and importance sampling, which only requires one set of input-output samples and the computational cost is independent of the dimensionality of inputs. The proposed method firstly uses importance sampling density function which can promise that a large number of samples will drop into the failure domain to generate a set of samples and then simultaneously obtain the sensitivity indices for all the input variables by repeatedly using this single set of samples. It is because of this that proposed method greatly improves the utilization of samples. Examples in this paper illustrate that our proposed method has higher efficiency, accuracy, convergence and robustness than the existing ones, and demonstrate its good prospect in engineering applications.