Presented is an efficient method for variance-based sensitivity analysis. It provides a general approach to transforming a sensitivity problem into one uncertainty propagation process, so that various existing approximation techniques (for uncertainty propagation) can be applied to speed up the computation. In this paper, formulations are deduced to implement the proposed approach with one specific technique named Univariate Reduced Quadrature (URQ). This implementation was evaluated with a number of numerical test-cases. Comparison with the traditional (benchmark) Monte Carlo approach demonstrated the accuracy and efficiency of the proposed method, which performs particularly well on the linear models, and reasonably well on most non-linear models. The current limitations with regard to non-linearity are mainly due to the limitations of the URQ method used.