Plastic pipe reinforced by cross helically wound steel wires, namely, PSP, is a new plastic-matrix steel composite pipe developed in China recently, were theoretically and experimentally investigated herein. Although the steel wires carry most of the loading in a linear elastic way, time-dependent behavior was demonstrated in PSP, and was then the subject of further analysis and description. Based on the structural features of PSP and the viscoelastic behaviors of the matrix, a three-layer viscoelastic model was proposed to identify time-dependent elastic stresses and strains for PSP subjected to internal pressure. The experimental results showed that the hoop strain decreased slowly, while the axial strain increased by 0.16% in 14,000 min at constant internal pressure. Good agreement between theoretical results and experimental data demonstrated that the three-layer viscoelastic model was able to predict the time-dependent relationship of stress and strain. Finally, the effects of the steel-wire volume fraction and the winding angle on the creep behavior of PSPs subjected to an internal pressure were analyzed.