This study introduces a simplified micromechanical model for analyzing a combined viscoelastic–viscoplastic response of unidirectional fiber reinforced polymer (FRP) composites. The micromechanical model is derived based on a unit-cell model consisting of fiber and matrix subcells. In this micromechanical model, a limited spatial variation of the local field variables in the fiber and matrix subcells is considered in predicting the overall time-dependent response of composites. The constitutive model for the polymer matrix is based on Schapery’s viscoelastic and Perzyna’s viscoplastic models. An incremental stress–strain relation is considered in solving the time-dependent and inelastic response. A linearized prediction and iterative corrector scheme are formulated to minimize errors from the linearization within the incremental stress–strain relation such that both the micromechanical constraints and the nonlinear constitutive equations are satisfied. The goal is to provide the accurate effective stress–strain relations of the composites and the corresponding viscoelastic and viscoplastic deformation in the polymeric matrix. The micromechanical model is verified by comparing the time-dependent response of the glass FRP composites having several off-axis fiber orientations with experimental data available in the literature.