This paper is concerned with Boolean satisfiability (SAT) Problem. Many researchers are devoted into seeking for new ideas as well as developing more efficient SAT solvers which will improve the development of EDA (Electronic Design Automation). In this paper, we try to solve the SAT problem by fuzzy genetic algorithm with partitioning-based initial process, namely PFGASAT. Some heuristic mechanisms have been introduced which make the algorithm more intellective. Primary experiments show that PFGASAT can solve SAT problems with more than 15k variables while behaves rather stably and robustly.