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This work presents a new method for obtaining the precise stationary state solutions of the Generalized Langevin Equation (GLE). The method combines Mori–Zwanzig formalism and diffusion approximation theory to provide an accurate analytical method for exploring the non-Markovian GLE. We demonstrate that the above-mentioned method can capture well the stationary state solutions of the GLE with memory kernel control and provide a valuable tool for studying the anomalous diffusion events. Numerical simulations confirm the accuracy of such Mori–Zwanzig formalism and diffusion approximation method. [ABSTRACT FROM AUTHOR]