Short read mapping is a process to align the short reads, which are fixed-length fragments of the target genome, to a given reference genome to identify the mutations in the target genome. Because of the rapid development of Next Generation Sequencing (NGS) technologies, faster short read mapping is required. In this paper, we propose an FPGA system for the short read mapping based on sort and parallel comparison of seeds. Seeds are fixed-length sub-strings in the short reads used to map the short read to the reference genome efficiently. In our system, (1) seeds are sorted using bucket sort, and the seeds in a bucket are compared in parallel with the candidate locations on the reference genome, (2) in this comparison, one nucleotide substitution, insertion, and deletion are allowed to achieve higher mapping rate, and (3) two stage search by reconfiguration is used to achieve higher performance. The mapping rate and search time by this approach outperforms existing systems.