Recently the stochastic kriging (SK) methodology proposed by Ankenman et al. (2010) has emerged as an effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. Although fruitful results have been achieved through bridging applications and theoretical investigations of SK, there lacks a unified account of efficient simulation experimental design strategies for applying SK metamodeling techniques. In this paper, we propose a sequential experimental design framework for applying SK to predicting performance measures of complex stochastic systems. This framework is flexible; i.e., it can incorporate a variety of design criteria. We propose several novel design criteria under the proposed framework, and compare the performance with that of classic non-sequential designs. The evaluation uses illustrative test functions and the well-known M/M/1 and the (s, S) inventory system simulation models.