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In climate models, subgrid parameterizations of convection and clouds are one of the main causes of the biases in precipitation and atmospheric circulation simulations. In recent years, due to the rapid development of data science, machine learning (ML) parameterizations for convection and clouds have been demonstrated to have the potential to perform better than conventional parameterizations. Most previous studies were conducted on aqua-planet and idealized models, and the problems of simulation instability and climate drift still exist. Developing an ML parameterization scheme remains a challenging task in realistically configured models. In this paper, a set of residual deep neural networks (ResDNNs) with a strong nonlinear fitting ability is designed to emulate a super-parameterization (SP) with different outputs in a hybrid ML–physical general circulation model (GCM). It can sustain stable simulations for over 10 years under real-world geographical boundary conditions. We explore the relationship between the accuracy and stability by validating multiple deep neural network (DNN) and ResDNN sets in prognostic runs. In addition, there are significant differences in the prognostic results of the stable ResDNN sets. Therefore, trial and error is used to acquire the optimal ResDNN set for both high skill and long-term stability, which we name the neural network (NN) parameterization. In offline validation, the neural network parameterization can emulate the SP in mid- to high-latitude regions with a high accuracy. However, its prediction skill over tropical ocean areas still needs improvement. In the multi-year prognostic test, the hybrid ML–physical GCM simulates the tropical precipitation well over land and significantly improves the frequency of the precipitation extremes, which are vastly underestimated in the Community Atmospheric Model version 5 (CAM5), with a horizontal resolution of 1.9 ∘ × 2.5 ∘. Furthermore, the hybrid ML–physical GCM simulates the robust signal of the Madden–Julian oscillation with a more reasonable propagation speed than CAM5. However, there are still substantial biases with the hybrid ML–physical GCM in the mean states, including the temperature field in the tropopause and at high latitudes and the precipitation over tropical oceanic regions, which are larger than those in CAM5. This study is a pioneer in achieving multi-year stable climate simulations using a hybrid ML–physical GCM under actual land–ocean boundary conditions that become sustained over 30 times faster than the target SP. It demonstrates the emerging potential of using ML parameterizations in climate simulations. [ABSTRACT FROM AUTHOR]