This paper represents a new efficient parallel implementation of neural networks on mesh-connected SIMD machines. A new algorithm to implement the recall and training phases of the multilayer feedforward network with backpropagation is devised. The developed algorithm is considered much faster than other known algorithms; it requires O(l) multiplications and O(logN) additions, whereas most others require O(N) multiplications and O(N) additions. In this paper we restrict the algorithm to map a neural network of a maximum of n neurons per layer on anN × Nmesh of processors whereN ≥ n, however, it may be extended to the general case. Time comparisons with other algorithms are furnished.