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Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition (POD)-Galerkin ROM when applied to the El Nino Southern Oscillation model, which integrates coupled atmosphere, ocean, and sea surface temperature (SST) mechanisms in the equatorial Pacific. While POD identifies the most energetic modes of a system from simulation data, the Galerkin projection maps the governing equations onto these reduced modes to derive a simplified dynamical system. Leveraging the unique coupling properties of the model, we propose a novel approach to formulate a reduced order model derived from Galerkin projection. Our approach achieves remarkable computational efficiency, requiring only four POD modes. The results provide highly stable and accurate solutions over 95% compared to the high-dimensional full-order model (FOM), highlighting the potential of POD-Galerkin reduction for efficient and accurate climate simulations.