There have been several attempts to understand the nature of the nucleon-nucleon interaction on the basis of the quark structure of the nucleon. In this work, the potential model approach is pursued. In particular, this project expands upon work done by P. D. Morley, D. L. Pursey, and S. A. Williams. They started with a basic interaction between quarks which was the sum of a phenomenological confining potential for quark confinement and a one-gluon-exchange potential inspired by QCD. This model led naturally to a nonlocal nucleon-nucleon interaction. In this thesis, a consistent local approximation to this nonlocal potential is presented. The local approximation lends itself to speedier calculations and should be more widely used than its nonlocal source. It should thus facilitate testing of the underlying assumptions of this QCD-derived model.