<p>Fluid-conveying pipes generally face combined excitations caused by periodic loads and random noises. Gaussian white noise is a common random noise excitation. This study investigates the random vibration response of a simply-supported pipe conveying fluid under combined harmonic and Gaussian white noise excitations. According to the generalized Hamilton’s principle, the dynamic model of the pipe conveying fluid under combined harmonic and Gaussian white noise excitations is established. Subsequently, the averaged stochastic differential equations and Fokker–Planck–Kolmogorov (FPK) equations of the pipe conveying fluid subjected to combined excitations are acquired by the modified stochastic averaging method. The effectiveness of the analysis results is verified through the Monte Carlo method. The effects of fluid speed, noise intensity, amplitude of harmonic excitation, and damping factor on the probability density functions of amplitude, displacement, as well as velocity are discussed in detail. The results show that with an increase in fluid speed or noise intensity, the possible greatest amplitude for the fluid-conveying pipe increases, and the possible greatest displacement and velocity also increase. With an increase in the amplitude of harmonic excitation or damping factor, the possible greatest amplitude for the pipe decreases, and the possible greatest displacement and velocity also decrease.</p>