In this paper, an attempt was made to extend the Differential Quadrature Method (DQM) to establish the nonlinear vibrations of a cantilevered pipe conveying fluid with motion-limiting nonlinear constraints. The partial differential equation of motion of the pipe was transformed to an ordinary differential equation by DQM. Based on this，attention was concentrated on the vibration behaviour of the free end of the pipe, and several vibrations were found by numerical calculations. Calculations of the bifurcation diagram, phase portraits of the motion, time histories and Poincaré maps establish definitively the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations of specific parameters. The represented results show reasonably good agreement with other classical ones. Thus it is demonstrated that the present method is valid and applicable for studying the dynamic response (including chaotic vibrations) of some other structures.