A critical challenge for machine-learning (ML) parameterization in global climate models (GCMs) is to achieve stable, accurate simulations under climates not seen during training. Previous studies have demonstrated promising offline performance and year-long online stability in aquaplanet simulations but have encountered difficulties in real geography and under climate warming. Here we report that a GCM with real geography configuration using neural-network-based cloud and convection parameterization, trained exclusively with present-day climate data, successfully performs a stable, decade-long simulation of a warm climate with +4 K sea surface temperature (SST). The neural network (NN) is based on Han et al. (2023, https://doi.org/10.1029/2022ms003508) with additional inputs. The simulation captures the global precipitation distribution, surface temperatures, vertical atmospheric structures, and extreme precipitation very well, closely matching simulations from both the superparameterized CAM (SPCAM) and the conventional CAM5 in the warm climate without accuracy degradation compared to those in the baseline climate. Moreover, it produces a climate response to +4 K SST in atmospheric thermodynamic states and circulations similar to those from SPCAM and CAM5. Prognostic ablation tests on NN input variables show that the NN without convective memory as input suffers from numerical instability, and the NN without considering radiative variables and land fraction as input, or with reduced training samples produce less accurate results. To our knowledge, this is the first time an ML parameterization successfully achieves online extrapolation to a warm climate without using additional warm-climate data for training. It demonstrates the potential of ML-driven parameterizations for credible long-term climate projections.