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A new type of deep neural networks (DNNs) is presented in this paper. Traditional DNNs use the multinomial logistic regression (softmax activation) at the top layer for classification. The new DNN instead uses a support vector machine (SVM) at the top layer. Two training algorithms are proposed at the frame and sequence-level to learn parameters of SVM and DNN in the maximum-margin criteria. In the frame-level training, the new model is shown to be related to the multiclass SVM with DNN features; In the sequence-level training, it is related to the structured SVM with DNN features and HMM state transition features. Its decoding process is similar to the DNN-HMM hybrid system but with frame-level posterior probabilities replaced by scores from the SVM. We term the new model deep neural support vector machine (DNSVM). We have verified its effectiveness on the TIMIT task for continuous speech recognition.