This paper presents the design of a systolic processor for DNA local pairwise alignment. The main building block of the processor is a 1D array of processing elements that allows pipeline processing to reduce the execution time with respect to software tools. We aligned two sequences of 4096 nucleotides from the ABO blood group gene of human and house mouse using ModelSim-Altera to verify the hardware design. The hardware simulation results were compared with software simulation results, showing the functionality of the design. The design can only be synthesized on the targeted FPGA for processing 256 nucleotides simultaneously due to hardware limitations (ALUTs and registers), but could be implemented for aligning larger sequences by using a bigger device or FPGA arrays. The design could also be used to implement other dynamic programming algorithms by modifying the processing element.