Graphics processing unit (GPU) has been applied successfully in many scientific computing realms due to its superior performances on float-pointing calculation and memory bandwidth, and has great potential in power system applications. The N-1 static security analysis (SSA) appears to be a candidate application in which massive alternating current power flow (ACPF) problems need to be solved. However, when applying existing GPU-accelerated algorithms to solve N-1 SSA problem, the degree of parallelism is limited because existing researches have been devoted to accelerating the solution of a single ACPF. This paper therefore proposes a GPU-accelerated solution that creates an additional layer of parallelism among batch ACPFs and consequently achieves a much higher level of overall parallelism. First, this paper establishes two basic principles for determining well-designed GPU algorithms, through which the limitation of GPU-accelerated sequential-ACPF solution is demonstrated. Next, being the first of its kind, this paper proposes a novel GPU-accelerated batch-QR solver, which packages massive number of QR tasks to formulate a new larger-scale problem and then achieves higher level of parallelism and better coalesced memory accesses. To further improve the efficiency of solving SSA, a GPU-accelerated batch-Jacobian-Matrix generating and contingency screening is developed and carefully optimized. Lastly, the complete process of the proposed GPU-accelerated batch-ACPF solution for SSA is presented. Case studies on an 8503-bus system show dramatic computation time reduction is achieved compared with all reported existing GPU-accelerated methods. In comparison to UMFPACK-library-based single-CPU counterpart using Intel Xeon E5-2620, the proposed GPU-accelerated SSA framework using NVIDIA K20C achieves up to 57.6 times speedup. It can even achieve four times speedup when compared to one of the fastest multi-core CPU parallel computing solution using KLU library. The proposed batch-solving method is practically very promising and lays a critical foundation for many other power system applications that need to deal with massive subtasks, such as Monte-Carlo simulation and probabilistic power flow.