Space-time adaptive processing (STAP) is an essential technique for such key applications as next generation airborne early warning and control system (AWACS) radars. In this paper, we develop an efficient GPU-accelerated solution for a complete STAP backend. Especially, we propose a data parallel procedure and its GPU implementation for the inversion of Hermitian matrices, which is the bottleneck of STAP. Our GPU solution achieves a speedup of up to 125X against its CPU counterpart and outperforms a FPGA implementation by a factor of over 20. The speedup can be translated to a higher computing throughput and/or an enhanced level of accuracy. The matrix inversion techniques can also be applied to other important scientific and engineering domains.