This research reports on the variation behavior of the bundle thickness in a fiber bundle flow process, when the stochastic perturbation occurs. The stochastic perturbation is specified by an autocorrelation function, which is generated on the basis of the random phase spectrum. The profiles of the bundle thickness and velocity in a steady state were simulated, while the mathematical model describing the fiber bundle flow dynamics is employed. Simulation results showed that a stochastic signal with a specified autocorrelation function could apply to variations in the fiber bundle parameter and draft ratio. The distribution profiles of the velocity and linear density of the fiber bundle were estimated under the auto-correlated perturbations. Disturbances in the material parameter revealed a larger influence on the dynamic states of the fiber bundle flow than those in draft ratio.