Dynamical models used in climate prediction often suffer from systematic errors that can deteriorate their predictions. We propose a hybrid model that combines both dynamical model and artificial neural network (ANN) correcting model errors to improve climate predictions. We conducted a series of experiments using the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM) and trained the ANN with input from both atmospheric and oceanic variables and output from analysis increments. Our results demonstrate that the hybrid model outperforms the dynamical model in terms of prediction skill for both atmospheric and oceanic variables across different lead times. Furthermore, we conducted additional experiments to identify the key factors influencing the prediction skill of the hybrid model. We found that correcting both atmospheric and oceanic errors yields the highest prediction skill while correcting only atmospheric or oceanic errors has limited improvement.