Abstract: In the realm of subsurface flow simulations, deep-learning-based surrogate models have emerged as a promising alternative to traditional simulation methods, especially in addressing complex optimization problems. However, a significant challenge lies in the necessity of numerous high-fidelity training simulations to construct these deep-learning models, which limits their application to field-scale problems. To overcome this limitation, we introduce a training procedure that leverages transfer learning with multi-fidelity training data to construct surrogate models efficiently. The procedure begins with the pre-training of the surrogate model using a relatively larger amount of data that can be efficiently generated from upscaled coarse-scale models. Subsequently, the model parameters are fine-tuned with a much smaller set of high-fidelity simulation data. For the cases considered in this study, this method leads to about a 75% reduction in total computational cost, in comparison with the traditional training approach, without any sacrifice of prediction accuracy. In addition, a dedicated well-control embedding model is introduced to the traditional U-Net architecture to improve the surrogate model's prediction accuracy, which is shown to be particularly effective when dealing with large-scale reservoir models under time-varying well control parameters. Comprehensive results and analyses are presented for the prediction of well rates, pressure and saturation states of a 3D synthetic reservoir system. Finally, the proposed procedure is applied to a field-scale production optimization problem. The trained surrogate model is shown to provide excellent generalization capabilities during the optimization process, in which the final optimized net-present-value is much higher than those from the training data ranges.