The nested-simulation is commonly used for calculating the predictive distribution of the total variable annuity (VA) liabilities of large VA portfolios. Due to the large numbers of policies, inner-loops and outer-loops, running the nested-simulation for a large VA portfolio is extremely time consuming and often prohibitive. In this paper, the use of surrogate models is incorporated into the nested-simulation algorithm so that the relationship between the inputs and the outputs of a simulation model is approximated by various statistical models. As a result, the nested-simulation algorithm can be run with much smaller numbers of different inputs. Specifically, a spline regression model is used to reduce the number of outer-loops and a model-assisted finite population estimation framework is adapted to reduce the number of policies in use for the nested-simulation. From simulation studies, our proposed algorithm is able to accurately approximate the predictive distribution of the total VA liability at a significantly reduced running time.