Abstract: Fluid-conveying pipes have been widely used in aerospace, petrochemical, offshore and other important engineering fields. The vibration characteristics of the fluid-conveying pipes, especially the natural characteristics of the system, have been an important issue in the research of scholars around the world. This study investigates the natural characteristics of transverse vibration of a fluid-conveying pipe with elastic supports at both ends. In particular, the natural characteristics of the fluid-conveying pipe with asymmetric elastic supports at both ends are discussed. The governing equation and boundary conditions of the fluid-conveying pipe system are derived by the Hamilton’s principle. The modal functions of the static pipe are obtained by the complex modal method, and then they are used as the potential function and weight function for the Galerkin method to truncate the control equation of the linear derived system. The effects of symmetrical support stiffness at both ends, asymmetric support stiffness at both ends, pipe length and fluid mass ratio on the natural frequencies of the system are discussed. The discussion focuses on the variation of natural frequencies under the condition of asymmetric supports that may happen at both ends of the pipe. Results show that a fast decrease in the first natural frequency for large symmetrical support stiffness. When the support stiffness at both ends of the pipe changes, the natural frequencies of each order of the pipe obtain the maximum or minimum value when the support stiffness at both ends is equal. For the pipe with asymmetric supports at both ends, the closer the support stiffness at both ends, the faster the first natural frequency decreases, and the smaller the corresponding critical flow velocity. The greater the flow velocity of the fluid, the more significant is the effect on the natural frequency of the pipe supported by asymmetric supports at both ends.