The electromyogram (EMG) signals from an individual’s muscles can reflect the biomechanics of human movement. The accurate classification of individual and combined finger movements using surface EMG signals is able to support many applications such as dexterous prosthetic hand control. The existing research of EMG-based hand gesture classification faces the challenges of inaccurate classification, insufficient generalization ability and weak robustness. To address these problems, this paper proposes a deep learning model that combines convolutional auto-encoder and convolutional neural network (CAE+CNN) to classify an EMG dataset consisting of 10 classes of hand gestures. The proposed method shrinks the inputs into a smaller latent space representation using CAE and the resultant compressed features are served as inputs of CNN, which reduces the redundancy of EMG signals and improves the classification accuracy and training efficiency. Besides, to enhance the robustness and generalization ability for classification, a data processing approach is proposed which combines the windowing method and majority voting of the obtained results from the classifier. In addition, comprehensive comparative study is carried out with 8 widely applied and state-of-the-art classifiers in terms of classification accuracy, robustness subject to noise and statistical analysis (sensitivity, specificity, precision, F1 Score and Matthews correlation coefficient). The results demonstrates that the integration of windowing method, CAE+CNN and majority voting achieves the best performance (99.38% test accuracy for the data without adding noise, which is 3.78% higher than the best classifier used for comparison), strongest robustness (achieved 98.13% test accuracy when Gaussian noise of level 1e-5 is added to the raw dataset, which is 4.07% higher than the best classifier used for comparison) and statistical properties compared to other classifiers, which shows the potential for healthcare applications such as movement intention detection and dexterous prostheses control.