Pairwise testing is an effective test generation technique that requires all pairs of parameter values to be covered by at least one test case. It has been proven that generating minimum test suite is an NP-complete problem. Genetic algorithms have been used for pairwise test suite generation by researchers. However, it is always a time-consuming process, which leads to significant limitations and obstacles for practical use of genetic algorithms towards large-scale test problems. Parallelism will be an effective way to not only enhance the computation performance but also improve the quality of the solutions. In this paper, we use Spark, a fast and general parallel computing platform, to parallelize the genetic algorithm to tackle the problem. We propose a two-phase parallelization algorithm including fitness evaluation parallelization and genetic operation parallelization. Experimental results show that our algorithm outperforms the sequential genetic algorithm and competes with other approaches in both test suite size and computational performance. As a result, our algorithm is a promising improvement of the genetic algorithm for pairwise test suite generation.