A holographic implementation for neural networks is proposed and demonstrated as an alternative to the optical matrix-vector multiplier architecture. In comparison, the holographic architecture makes more efficient use of the system space-bandwidth product for certain types of neural networks. The principal network component is a thermoplastic hologram, used to provide both interconnection weights and beam redirection. Given the updatable nature of this type of hologram, adaptivity or network learning is possible in the optical system. Two networks with fixed weights are experimentally implemented and verified, and for one of these examples we demonstrate the advantage of the holographic implementation with respect to the matrix-vector processor.