To improve the classification accuracy of hyperspectral remote sensing images, a classification algorithm based on a multiscale convolutional neural network (CNN) is proposed. First, an isometric feature mapping algorithm was used to process hyperspectral data, to mine the nonlinear characteristics of the data and maintain the intrinsic geometric properties of data points. Second, training image blocks centered on labeled pixels were constructed, after which the multiscale CNNs were trained. Finally, the Softmax classifier was used to predict the label of the test pixel. The proposed method performed classification experiments on the Indian Pines, University of Pavia, and Salinas scene hyperspectral remote sensing datasets, and its performance was compared with a CNN, randomized principal component analysis (R-PCA CNN), a deep CNN with pixel-pair features (CNN-PPF), a cross-domain CNN (CD-CNN), and other algorithms. The experimental results showed that the overall recognition accuracy of the proposed method for the three datasets was 98.51%, 98.64%, and 99.39%, respectively, which was 8.35%, 6.37%, and 7.81% higher than that of the CNN algorithm, respectively. The proposed method performed better than the other four methods studied, in terms of both classification accuracy and Kappa coefficient, providing a superior method for hyperspectral remote sensing data classification.