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We present a theoretical and experimental analysis of a mid-infrared wavelength-tunable cascade gain modulation Raman fiber laser. Our simulation model incorporates the Generalized Nonlinear Schrödinger Equation with the fiber Bragg grating transmission functions. Utilizing the pulse tracking method, we investigate and analyze the impact of pump pulse width and Raman gain fiber length on the first and second order Raman laser thresholds. Additionally, we exhibit the evolution process of the pulse and optical spectrum at a constant pump pulse energy. Furthermore, we present the output pulse width and energy, and the Raman laser center wavelength as a function of the pump pulse energy. Subsequently, using the optimal theoretical values of pump pulse width and Raman gain fiber length, we experimentally achieve the gain modulation Raman fiber laser. With a 1990 nm laser pumping, the Raman laser can produce a 2172 nm laser with a pulse width of 1.25 µs and a single pulse energy of approximately 400 nJ. When tuning the pump laser wavelength from 1950 nm to 2030 nm, the gain modulation Raman laser wavelength can vary from 2130 nm to 2215 nm. Importantly, our experimental results closely align with the theoretical predictions. This study provides valuable insights for the investigation of gain modulation Raman fiber lasers. [ABSTRACT FROM AUTHOR]