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Hybrid modeling combining data-driven techniques and numerical methods is an emerging and promising research direction for efficient climate simulation. However, previous works lack practical platforms, making developing hybrid modeling a challenging programming problem. Furthermore, the lack of standard data sets and evaluation metrics may hamper researchers from comprehensively comparing various algorithms under a uniform condition. To address these problems, we propose a framework called NeuroClim for hybrid modeling under the real-world scenario, a basic setting to simulate the real climate that we live in. NeuroClim consists of three parts: (1) Platform. We develop a user-friendly platform NeuroGCM for efficiently developing hybrid modeling in climate simulation. (2) Dataset. We provide an open-source dataset for data-driven methods in hybrid modeling. We investigate the characteristics of the data, i.e., heterogeneity and stiffness, which reveals the difficulty of regressing climate simulation data; (3) Metrics. We propose a methodology for quantitatively evaluating hybrid modeling, including the approximation ability of machine learning models and the stability during simulation. We believe that NeuroClim allows researchers to work without high level of climate-related expertise and focus only on machine learning algorithm design, which will accelerate hybrid modeling research in the AI-Climate intersection. The codes and data are released at https://github.com/x-w19/NeuroClim.