This paper describes an implementation of the combined hybrid‐parallel prediction (CHyPP) approach of Wikner et al. (2020), https://doi.org/10.1063/5.0005541 on a low‐resolution atmospheric global circulation model (AGCM). The CHyPP approach combines a physics‐based numerical model of a dynamical system (e.g., the atmosphere) with a computationally efficient type of machine learning (ML) called reservoir computing to construct a hybrid model. This hybrid atmospheric model produces more accurate forecasts of most atmospheric state variables than the host AGCM for the first 7–8 forecast days, and for even longer times for the temperature and humidity near the earth's surface. It also produces more accurate forecasts than a model based only on ML, or a model that combines linear regression, rather than ML, with the AGCM. The potential of the CHyPP approach for climate research is demonstrated by a 10‐year long hybrid model simulation of the atmospheric general circulation, which shows that the hybrid model can simulate the general circulation with substantially smaller systematic errors and more realistic variability than the host AGCM.