Due to the heterogeneity and uncertainty of the reservoir, it is very challenging to select the best oil, gas, and water components to calculate the reservoir production, and it cannot meet the real-time requirements. By changing the production constraints of the well, a Radial Basis Neural Network Reservoir Model (RBNNRM) for a Multi-stage Fracturing Horizontal Well (MFHW) is proposed to predict the Bottom Hole Flowing Pressure (BHFP). First, a reservoir model of a multi-stage fractured horizontal well is established and laboratory self-developed production data analysis software is used to calculate the BHFP. Second, part of the obtained data are imported into the neural network model as training data. In the training process, according to the results obtained from the test data, the network parameters are constantly adjusted to obtain the most optimized network model. Third, the resulting neural network is tested using the remaining data. Finally, a field case of a multi-stage fracturing horizontal well is studied by using the presented RBNNRM neural network model. The results show that in most cases, the proposed model performs better than other models, with the highest accuracy and the lowest root mean square error. This proves that the RBNNRM can be effectively applied to the BHFP prediction of the MFHW. The experimental results also show that, compared with the traditional pressure calculation reservoir model, the use of the RBNNRM to calculate the BHFP can achieve a speedup of dozens of times, which can meet the needs of field calculations.