Abstract: In order to better understand the short-term and long-term deformation behaviors of carbon fiber reinforced epoxy (CF/EP) composite materials, a series of tensile creep tests of a type of CF/EP laminated composite material under constant loads, typically, 20%, 30% and 40% of ultimate tensile strength and constant temperatures (25°C and 50°C) were conducted. The material deforms in a remarkable time-dependent way, and behaves both clearly creep temperature effect and physical aging phenomena. Specifically, the tensile strains increase during the short time duration after the tests begin, similar to creep deformation. When the testing time exceeds physical aging characteristic time, the tensile strains start to decrease during the most of loading period. To characterize reasonably this particular deformation behavior, a linear viscoelastic model was developed to describe both creep temperature effect and physical ageing effect. The related viscoelastic constitutive relations of this composite material were derived, and further numerically implemented using the Prony series. In addition, its numerical algorithm was proposed within a finite element framework, and numerical analysis was performed via UMAT subroutine. The new theoretical model is then verified by a comparison of experimental results to numerical ones.