A capsule network (CapsNet) is a novel neural network that has been widely used in the classification of hyperspectral remote sensing. However, it is faced with overfitting and gradient vanishing. To solve this problem, this paper proposes a hyperspectral remote sensing classification method using a multi-scale adaptive capsule network (MSCaps). The multi-scale convolution layer was used to extract the spatial and spectral features of the ground object from the input images with different sizes (namely, multi-scale). To solve the overfitting problem caused by the sparseness of the coupling coefficient $c_{ij}$, we applied an adaptive routing algorithm without iteration to further improve the CapsNet structure. To validate the proposed model, we evaluated the classification performances of MSCaps using overall classification accuracy (OA) and model training efficiency on two public hyperspectral remote sensing datasets, namely, the Pavia University (PU) and Salinas-A (SA) datasets. The OA of MSCaps was measured and compared with that of the benchmarks, including support vector machine (SVM), random forest (RF), deep convolutional neural network (CNN), CapsNet, multi-scale capsule network (MCaps), capsule network using adaptive routing algorithm without iteration (ARWI-Caps), and the multi-scale CNN (MSCNN) on original images. Additionally, the OA of MSCaps was compared with that of SVM and RF on images extracted using principal component analysis (PCA). They are named PCA-SVM and PCA-RF, respectively. The training efficiency of MSCaps was compared with that of CNN, CapsNet, and MSCNN. The experimental results show that the OA of CapsNet on the PU and SA datasets is 99.14% and 95.38%, respectively, which is higher than that of the benchmarks. Additionally, the training time of MSCaps is ~1/3 and ~1/4 of that of CapsNet on the PU and SA datasets, respectively. Thus, the training efficiency of MSCaps is significantly higher than that of CapsNet. Therefore, the proposed hyperspectral remote sensing classification method using MSCaps has a good application potential and is an effective alternative for hyperspectral remote sensing classification.