The effect of maleic anhydride grafted polypropylene (MAPP) coupling agents on properties of a new composite made of recycled carbon fibers and recycled polypropylene (rCF/[rPP + MAPP]) was studied experimentally. This new material presented significantly improved properties, compared to the previous generation, without the addition of MAPP (Giannadakis K, Szpieg M and Varna J. Mechanical performance of recycled carbon fibre/PP. Exp Mech 2010; published online.). This was mostly attributed to improvement of the fiber/matrix interface. The inelastic and time-dependent behavior of the MAPP modified composite material in tension was analyzed. A series of quasi-static tensile and creep tests were performed to identify the material model, which accounts for: (a) damage-related stiffness reduction, (b)development of stress and time-dependent irreversible strains described as viscoplasticity, (c) nonlinear viscoelastic behavior. The damage-related stiffness reduction was found to be less than 10%. Although damage-dependent stiffness was not the main source of nonlinearity, it was included in the inelastic material model. In creep tests, it was found that the time and stress dependence of viscoplastic strains follows a power law, which makes the determination of the parameters in the viscoplasticity model relatively simple. The viscoelastic response of the composite was found to be linear in the investigated stress domain. The material model was validated in constant stress rate tensile tests.