Structural components made of fiber-reinforced polymer composites require service life that is sometimes decades long. Time-dependent deformation of the composite material can endanger their structural performance, even when subjected to stress levels well below the material strength. Therefore, the development of reliable simulation tools to predict the long-term behavior of composites is of great importance. In this contribution a micromechanical framework for modeling off-axis creep rupture in unidirectional (UD) composites undergoing finite strains is presented. The numerical model is a thin slice representative volume element (RVE) defined in coordinate system aligned with the reinforcement direction. Off-axis loading is imposed on the RVE following the formulation details introduced in. Creep deformation, which has its roots in the viscosity of the polymer matrix, is represented with the Eindhoven Glassy Polymer (EGP) material model. Since it is not possible to predict the creep rupture time with the EGP model, the RVE is supplemented with a cohesive zone model. For this purpose, a cohesive microcrack initiation criterion based on the critical free energy stored in the polymer matrix is proposed, as well as a time-dependent cohesive law. The composite material is considered to fail when the homogenized creep strain-rate attains a minimum value. Simulation results are compared with experiments on UD thermoplastic carbon/PEEK composite tapes tested at different off-axis angles, stress levels and temperatures. Creep deformation obtained by the model matches well with the experimental observation. Although the trend of the creep rupture time decreasing with an increase in the stress is captured by the model, there is an offset in the actual values when compared with the experiment. As the material sustains finite deformations, the composite microstructure changes orientation in the loading process. The effect of this reorientation on the creep response is assessed with RVE simulations.