The development of smart grid and the increasing scale of power system brings more and more pressure to the conventional power system simulators. The graphic processing unit which features the massive concurrent threads and excellent floating point performance brings a new chance to the area of power system simulation. This paper introduces a hierarchical parallel LU decomposition algorithm based on stratified elimination tree, and develops a graphic processing unit (GPU)-based parallel linear system solver on the algorithm. To boost the effectiveness of the solver, a hybrid improved matrix ordering algorithm is proposed which can reduce the height of the elimination tree. On the basis of the solver, this paper implements a coarse-grained task parallelism which can analyze several contingencies of static security assessment (SSA) in parallel, and develops a two-layered parallel SSA program. The performance of the proposed parallel SSA program is benchmarked on a Tesla C2050 GPU using several real world cases, whose scale is up to 21801 nodes, compared with a serial SSA program which runs on a Xeon E5620 CPU. The results of the case studies show that the introduced method's speedup reaches 9.2 times, which can greatly accelerate SSA solution.