In this paper we propose the Structured Deep Neural Network (structured DNN) as a structured and deep learning framework. This approach can learn to find the best structured object (such as a label sequence) given a structured input (such as a vector sequence) by globally considering the mapping relationships between the structures rather than item by item. When automatic speech recognition is viewed as a special case of such a structured learning problem, where we have the acoustic vector sequence as the input and the phoneme label sequence as the output, it becomes possible to comprehensively learn utterance by utterance as a whole, rather than frame by frame. Structured Support Vector Machine (structured SVM) was proposed to perform ASR with structured learning previously, but limited by the linear nature of SVM. Here we propose structured DNN to use nonlinear transformations in multi-layers as a structured and deep learning approach. This approach was shown to beat structured SVM in preliminary experiments on TIMIT.