Pipelines located on the decks of FPSO systems are exposed to damage due to sea wave induced random loading. In this context, a methodology for estimating the fatigue life of fluid-conveying pipelines is presented. The pipeline is subjected to a random support motion that simulates the effect of the FPSO heaving. The equation of motion of the pipeline is derived by assuming small amplitude displacements, modeling the empty pipeline as a Bernoulli-Euler beam, and adopting the so-called “plug-flow” approximation for the fluid (Fluid-Structure Interactions Slender Structures and Axial Flow, Academic Press, San Diego, Vol. 1). Random vibration analysis is carried out by the Galerkin method selecting as basis functions the natural modes of a beam with the same boundary conditions as the pipeline. The discretized equations of motion are used in conjunction with linear random vibration theory to compute the stress spectrum for a generic section of the pipeline. For this purpose, the power spectrum of the acceleration at the deck level is determined by using the Response Amplitude Operator of the FPSO hull. Finally, the computed stress spectrum is used to estimate the pipeline fatigue life employing an appropriate S-N fatigue curve of the material. An illustrative example concerning a pipeline simply supported at both ends is included in the paper.