Oil saturation is a kind of spatiotemporal sequence that changes dynamically with time, and it is affected not only by the reservoir properties, but also by the injection–production parameters. When predicting oil saturation during water and gas injection, the influence of time, space and injection–production parameters should be considered. Aiming at this issue, a prediction method based on a controllable convolutional long short-term memory network (Ctrl-CLSTM) is proposed in this paper. The Ctrl-CLSTM is an unsupervised learning model whose input is the previous spatiotemporal sequence together with the controllable factors of corresponding moments, and the output is the sequence to be predicted. In this way, future oil saturation can be generated from the historical context. Concretely, the convolution operation is embedded into each unit to describe the interaction between temporal features and spatial structures of oil saturation, thus the Ctrl-CLSTM realizes the unified modeling of the spatiotemporal features of oil saturation. In addition, a novel control gate structure is introduced in each Ctrl-CLSTM unit to take the injection–production parameters as controllable influencing factors and establish the nonlinear relationship between oil saturation and injection–production parameters according to the coordinates of each well location. Therefore, different oil saturation prediction results can be obtained by changing the injection–production parameters. Finally, experiments on real oilfields show that the Ctrl-CLSTM comprehensively considers the influence of artificial controllable factors such as injection–production parameters, accomplishes accurate prediction of oil saturation with a structure similarity of more than 98% and is more time efficient than reservoir numerical simulation.