At present, there are many methods for the estimation of global reliability sensitivity. However, these methods cannot efficiently and accurately estimate the global reliability probability in case of small failure probability (10^{-4} or smaller). In this work, a highly efficient method to compute the global reliability sensitivity is proposed for the small failure probability. The proposed method combines the space-partition (SP) with unscented transformation (UT) which can obtain the first two moments of lowly nonlinear response function. The importance sampling density function, which is constructed by increasing the standard deviation, is employed to partition the input space into a series of subspaces, and thus the subspaces partitioned by the constructed importance sampling density function can move to the important area for the failure probability. Because the complexity of response function is reduced in the partitioned subspace, in which UT can estimate effectively the failure probability, the proposed method can estimate the global reliability sensitivity indices efficiently. All the above contribute to the efficiency and accuracy of the proposed method to compute the global reliability sensitivity. In this paper, the proposed method is compared with the existing methods and examples, and it is shown that the proposed method outperforms the others.