This paper investigates a stochastic economic emission dispatch (SEED) problem considering variable wind power integration and transforms this problem into an equivalent large-scale bi-objective deterministic optimization model based on the scenario method. It simultaneously minimizes power purchase costs and polluting gas emissions. The normal boundary intersection (NBI) method is introduced to convert the bi-objective optimization (MOO) model into a series of single-objective optimization (SOO) problems, which are solved using the interior-point method (IPM). In the process of solving each SOO problem, this paper rearranges the coefficient matrix of the correction equation in the block bordered diagonal form (BBDF) according to the sequence of the forecast scenario and sampling scenarios. Thus, it is able to decompose this correction equation further into a number of low-dimensional equations corresponding to the forecast scenario and sampling scenarios, respectively, and solve them using the asynchronous block iteration method. Furthermore, the proposed algorithm is implemented on a real provincial power system, and a parallel computational framework is built on high-performance clusters to demonstrate the enhancements in computational speed and the reduced memory requirements obtained by parallelization. Through this framework, scheduling of the outputs of generators on a day-ahead basis can be obtained. In addition, itindicates that the comprehensive compromised optimal solution can be used as an optimal dispatching scheme of power system operation.