The building of flow surrogate models is the frontier of simulation technology research for oil and gas reservoirs.However，the currently widely used pure data-driven flow surrogate models have no theoretical support and require a high data volume and data quality，which greatly limits the development of flow surrogate models. Therefore，this paper proposes a flow surrogate model based on a data-driven and physics-driven method. On the basis of the pure data-driven flow surrogate model，it takes advantage of the flow theory to simulate and predict oil and gas flow processes. Firstly，the dual-driven flow surrogate model is compared with the pure data-driven model. The results show that the proposed model can still maintain high prediction accuracy even if the training data is extremely sparse. Secondly，the robustness of the dual-driven model is explored by adding different levels of noise interference to the training data，and it is verified that the proposed model outperforms the pure data-driven flow surrogate model. Finally，the trained dual-driven flow surrogate model is applied to a new flow field through transfer learning. The model can achieve rapid convergence and save computing resources.