The pipelined structures for computing the B-spline curve is described. Various representations of the B-spline curve are explored first. Then, their pipelined architectures for computing the B-spline curve are implemented. In comparison with previous approach, the method used in the paper is more precise with the analysis of computational complexity in every computational environment and the performance improvement is in accordance with the experimental result of previous approach. It is also interesting to note that the recursive B-spline representation is a better one in the pipelined environment. This situation, however, is totally reversed in the single processor environment The INMOS transputer development system is used to verify the pipelined algorithms developed in the paper.