Injecting CO2 into the reservoir can not only improve crude oil recovery but also achieve the goal of CO2 geological storage. It can not only reduce the greenhouse effect but also obtain additional economic benefits. From the perspective of minimum miscible pressure, carbon dioxide flooding can be divided into miscible flooding and immiscible flooding, and miscible flooding is widely used in the oil field. The most important condition for miscible flooding is to achieve the minimum miscible pressure (MMP). In the study, combining the particle swarm optimization (PSO) with Gaussian process regression (GPR), a novel intelligent GPR and particle swarm optimization (GPR-PSO) method was proposed to establish the model of predicting the MMP of the CO2 and oil system. The model uses the database with more data than in the previous literature, with 365 data points, and the value range of the data is also wider. Moreover, the accuracy of GPR-PSO model was evaluated by statistical error and graph error and compared with the prediction results of existing models. The results show that compared with other models, the GPR-PSO model has higher accuracy and wider application range, the mean absolute relative error is only 1.66%. Meanwhile, the reliability of the model is verified by the sensitivity analysis of parameters. The results show that the most influential parameter on the prediction results is the reservoir temperature, and the least influential parameter is the critical temperature of injected gas. The GPR-PSO model can be used not only to predict the MMP of CO2 and oil system but also to predict the MMP of other gases and crude oil system.