Many DNA sequence analysis tools have been developed to turn the massive raw DNA sequencing data generated by NGS (Next Generation Sequencing) platforms into biologically meaningful information. The pair-HMMs forward algorithm is widely used to calculate the overall alignment probability needed by a number of DNA analysis tools. In this paper, we propose a novel systolic array design to accelerate the pair-HMMs forward algorithm on FPGAs. A number of architectural features have been implemented to improve the performance of the design, such as early exit points to increase the utilization of the array for small sequence sizes, as well as on-chip buffering to enable the processing of long sequences effectively. We present an implementation of the design on the Convey supercomputing platform. Experimental results show that the FPGA implementation of the pair-HMMs forward algorithm is up to 67x faster, compared to software-only execution.