Considering the environmental damping, this paper investigated the chaotic vibrations of a KelvinVoigt type curved pipe conveying fluid subjected to motionlimiting constraint. Numerical simulations indicate that the chaotic vibrations can be induced for certain parameter values of the curved pipe conveying fluid, and the environmental damping and viscoelastic coefficient greatly affect the dynamic responses of the curved pipe. The results provided a reference for tubing and design of pipe system in engineering applications.