Geologic carbon storage (GCS) entails injecting large volumes of carbon dioxide (CO2) in deep geologic formations to prevent its release to the atmosphere. Reservoir simulation is widely used in GCS applications to predict subsurface pressure and CO2 saturation. High fidelity numerical models are prohibitively expensive for data assimilation and uncertainty quantification, which require a large number of simulation runs. Deep learning-based surrogate models have shown a great promise to alleviate the high computational cost. However, the training cost is high as thousands of high-fidelity simulations are often necessary for generating the training data. In this work, we explore the use of a transfer learning approach to reduce the training cost. Compared with the surrogate model trained with high-fidelity simulations, our new transfer learning-based model shows comparable accuracy but reduces the training cost by 80%.