Abstract: The vibration characteristics of a pinned-pinned fluid-conveying pipe under various supported angles are investigated. The motion equations are established for the pinned-pinned fluid-conveying pipe with a supported angle θ. When any motion constraint is not imposed on the pipe, the bifurcation diagram of vibration response of the pipe is presented, from which the evolving characteristics of the response are analyzed. In comparison with the case of the pipe without any motion constraint, the effects of gravity parameter and motion constraint on the vibration response of the pipe are discussed in more detail. It is shown that the bifurcation phenomenon is very common when the supported angle changes, and a proper motion constrain can moderately reduce the vibration amplitude of the pipe. Moreover, a larger gravity parameter will lead to a simpler response, and in practice, the vibration characteristics can be adjusted by changing the values of corresponding parameters.