The ultimate goal of vector quantization (VQ) is to encode the signal into representative code vectors such that it can be represented digitally in a compact way. This task can be formulated as an optimization problem, namely the minimization of the total distance between the signal and the code vectors. In this paper, we formulate VQ as a constrained binary integer programming problem by eliminating the code vectors, where the constraints that partition the signal space are linear. We propose a two dimensional Gradient Network to solve this problem. The performance of this solution method is tested on image compression applications and the results are compared with the ones obtained by the well-known k-means algorithm.