Current hyperspectral classification algorithms cannot satisfy the requirements of high accuracy and low energy consumption of on-board classification simultaneously. A hyperspectral on-board classification algorithm based on multiscale spatial feature extraction is proposed to solve this problem. The proposed algorithm can significantly reduce the computational costs of the algorithm while maintaining high classification accuracy. Local maximum filtering is used to extract the texture features of hyperspectral images. The multiscale filtering results are combined with the spatial correlation of remote-sensing images to obtain joint local-global spatial features. After the spatial and spectral features are fused, the random forest is used for classification. The algorithm only includes integer comparison and addition operations and does not use high overhead operations, such as multiplication and exponentiation, in mainstream hyperspectral classification algorithms. Experimental results on Indian Pines, Pavia University, and HyRANK image datasets show that the algorithm's classification accuracy loss is within 2.4% compared with the highest-level classification algorithm. In addition, the proposed algorithm achieves high classification accuracy in cross-scene classification. The energy consumed in the classification process is reduced to less than 1/10000 compared with the on-board classification algorithm. Compared with existing algorithms, this algorithm is more suitable for on-board classification tasks and can effectively reduce the computational overhead and energy consumption during the on-board classification process while maintaining high classification accuracy.