This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.