In this paper, an anisotropic viscoelastic-viscoplastic macro-mechanical model is presented for short-fiber reinforced polymers. In addition to the rate-dependent response of the polymer matrix, fiber orientation leads to elastic and plastic anisotropy in short-fiber composites. The dependence of the yield stress on the strain rate and on the orientation is modeled by use of the Hill equivalent stress and the Eyring flow rule. Uniaxial tests at various strain rates were performed on injection molded samples cut at different orientations with respect to the mold flow direction. The test results show that the effects of strain rate and material orientation on yield stress are factorizable. The model aims to capture this behavior, which simplifies the characterization process. First, the model with a single relaxation time is presented and then the model is extended to multiple relaxation times to improve the predictions in the pre-yield regime. An efficient method for finding the model parameters for different modes is presented. An implicit scheme is used for the integration of the constitutive equations and the derivation of the consistent tangent stiffness tensor is presented. The model is implemented as an ABAQUS user material (UMAT) subroutine and is validated through comparison of the simulation results with the experiments.