In this paper, an automatic synthesis system FP/B of systolic array is presented, in which FP algebra and rewriting system are essentially used. Some concurrent functional forms are proposed, the expansion solutions of a class of linear recursive equations can be expressed by them directly. Algorithms which can be transformed into them may have efficient and regular computing structures, so parallelism and pipelinability hidden in the original algorithms are well developed. Based on the FP/B algebra we've given the formal defintion of systolic arrays and constructed a sys totolic rewriting system with properties of termitation and correctness.FP/B user programs can be automatically rewriten into equivalent optimized systolic expressions,Which can be directly mapped into VLSI architectures according to the geometric meanings of FP/B functions and concurrent functional forms.Finally,a typical instance is given to show the synthesis process.