Neural networks are powerful solutions to many scientific applications; however, they usually require long model training time due to large training data sets or large model size. Research has been focused on developing numerical optimization algorithms and parallel processing to reduce the training time. In this work, we propose a multi-resolution strategy that can reduce the training time by training the model with the reduced-resolution data samples at the beginning and later switching to the original resolution data samples. This strategy is motivated by the observation that coarser versions of many applications can be solved faster than their denser counterparts, and the solution to a coarser problem could be used to initialize the solution to the denser problem. When applying the idea to neural network training, coarse data can have a similar effect on the learning curves at the early stage as the dense data but requires less time. Once the curves no longer improve significantly, our strategy switches to using the data in original resolution. The key in this process is the ability to generate multiple resolutions of a problem automatically, which could usually be done with scientific applications with spatial and temporal continuity. We use two real-world scientific applications, CosmoFlow and DeepCAM, to evaluate the proposed mixed-resolution training strategy. Our experiment results demonstrate that the proposed training strategy effectively reduces the end-to-end training time while achieving a comparable accuracy to that of the training only with the original data. While maintaining the same model accuracy, our multi-resolution training strategy reduces the end-to-end training time up to 30% and 23% for CosmoFlow and DeepCAM, respectively.