The reliance on data and the high cost of data labelling are the main problems facing deep learning today. Active learning aims to make the best model with as few training samples as possible. Previous query strategies for active learning have mainly used the uncertainty and diversity criteria, and have not considered the data distribution's multi-granularity. To extract more valid information from the samples, we use three-way decisions to select uncertain samples and propose a multi-granularity active learning method (MGAL). The model divides the unlabeled samples into three parts: positive, negative and boundary region. Through active iterative training samples, the decision delay of the boundary domain can reduce the decision cost. We validated the model on five UCI datasets and the CIFAR10 dataset. The experimental results show that the cost of three-way decisions is lower than that of two-way decisions. The multi-granularity active learning achieves good classification results, which validates the model. In this case study, the reader can learn about the ideas and methods of the three-way decision theory applied to deep learning.