In order to understand the vibration characteristics of slightly curved fluid-conveying pipe under external excitation, a nonlinear vibration equation of slightly curved fluid-conveying pipe was established based on the Hamiltonian principle, and the vibration equations into a system of nonlinear ordinary differential equations was discretized by using the Galerkin truncation method. The nonlinear dynamic response of the system was solved by the incremental harmonic balance method. The stability and bifurcation behavior of the system response was studied by the Floquet theory. The research results indicate that the slightly curved fluid-conveying pipe exhibit both the soft-spring and the hard-spring characteristics under certain parameters. The analysis of the impact of system parameters on response indicates that as the initial rise of pipe increases, the response characteristics of the system change from the hardspring characteristics to the soft-spring characteristics. It can be seen that the curved configuration of pipe has a significant impact on the vibration characteristics of the fluid-conveying pipe, so the influence of initial imperfect of pipe must be considered in the design of the fluid-conveying pipe.