This paper presents an efficient parallel implementation and its performance evaluations of a SOFM neural netowrk on the multicomputer. We investigate the parallel performance as the size of a neural network N, the number of the patterns L, and the number of the processors p increase. We propose an analytica performance evaluation model for eac of the parallel implementations and verified the validity of the model through experiments. Analytical result show that the number of processors for a maximum speedup of the network decomposition nd the training-set decomposition increases in proportion to .root.N and .root.L, respectively. The performances of the both decompositions depend on the number of training patterns L and the size of the neural network N and, if L.geq.0.423N, the performance of trhe training-set decomposition is proved to be better than that of the network decomposition.