Hyperspectral imaging (HSI) classification has drawn tremendous attention in the field of Earth observation. In the big data era, explosive growth has occurred in the amount of data obtained by advanced remote sensors. Inevitably, new data classes and refined categories appear continuously, and such data are limited in terms of the timeliness of application. These characteristics motivate us to build an HSI classification model that learns new classifying capability rapidly within a few shots while maintaining good performance on the original classes. To achieve this goal, we propose a linear programming incremental learning classifier (LPILC) that can enable existing deep learning classification models to adapt to new datasets. Specifically, the LPILC learns the new ability by taking advantage of the well-trained classification model within one shot of the new class without any original class data. The entire process requires minimal new class data, computational resources, and time, thereby making LPILC a suitable tool for some time-sensitive applications. Moreover, we utilize the proposed LPILC to implement fine-grained classification via the well-trained original coarse-grained classification model. We demonstrate the success of LPILC with extensive experiments based on three widely used hyperspectral datasets, namely, PaviaU, Indian Pines, and Salinas. The experimental results reveal that the proposed LPILC outperforms state-of-the-art methods under the same data access and computational resource. The LPILC can be integrated into any sophisticated classification model, thereby bringing new insights into incremental learning applied in HSI classification.