We present the design of a planar-integrated optoelectronic vector-matrix multiplier. The inherent parallel-processing potential is fully exploited by optical implementation of multiplications and summations. Planar integration makes the free-space optical system compatible with electronic VLSI technologies. It is composed of phase-only diffractive optical elements, which implement lens and multiple-beam-splitter functions. A demonstrator version of the optical system for a matrix of size 10 x 10 was fabricated on quartz glass by means of multimask lithography and reactive ion etching. It shows low cross talk and good uniformity of the signals.