Dynamical models used in climate prediction often have systematic errors that can deteriorate predictions. In this study, we work in a twin experiment framework with a reduced-order coupled ocean-atmosphere model and aim to demonstrate the benefit of machine learning for climate prediction. Machine learning is applied to learn the model error and thus build a data-driven model to emulate the dynamical model error. Then we build a hybrid model by combining the data-driven and dynamical models. The prediction skill of the hybrid model is compared to that of the standalone dynamical model. We applied this approach to the ocean-atmosphere coupled model. The results show that the hybrid model outperforms the dynamical model alone for both atmospheric and oceanic variables. Also, we build two other hybrid models only correcting either atmospheric errors or oceanic errors. It was found that correcting both atmospheric and oceanic errors leads to the best performance.