In order to efficiently and accurately estimate the variance-based global sensitivity indices, especially for highly nonlinear response functions, a new method was proposed by combining the additive property of integration region and the UT (unscented transformation). Because the nonlinearity of response function is reduced in the local sub-space, in which the UT can explore the probability space very efficiently, the proposed method can estimate the variance-based sensitivity indices effectively. Moreover, the proposed method can estimate all the indices by using the same set of UT samples, and the approximate solution converges to the actual value with the increased number of divided subspace. The results of the nonlinear test example and the engineering example illustrate the efficiency and accuracy of the proposed method.