Uniaxial tension–unloading recovery, creep-recovery, and stress-controlled cyclic tests are first performed to investigate the recoverable viscoelasticity and irrecoverable viscoplasticity (including the uniaxial ratchetting) of ultrahigh molecular weight polyethylene (UHMWPE) polymer at room temperature. The results show that obvious time-dependent ratchetting occurs in the asymmetrical stress-controlled cyclic tension–compression and tension–tension tests of the UHMWPE, and total ratchetting strain consists of both recoverable viscoelastic and irrecoverable viscoplastic parts. Based on the experimental observation, a new viscoelastic–viscoplastic constitutive model is proposed to describe the time-dependent ratchetting of the UHMWPE. In the proposed model, the viscoplastic strain is set to be contributed simultaneously by the unified viscoplastic and creep ones. Meanwhile, a memory surface is introduced into the viscoelastic model to improve the description to the shapes of stress–strain hysteresis loops. Finally, the proposed model is verified by comparing the predictions with the corresponding experimental results of the UHMWPE. It is clearly demonstrated that the proposed model predicts the creep, viscoelastic recovery, and uniaxial time-dependent ratchetting of the UHMWPE well.