Early classification on multivariate time series is an important research topic in data mining with wide applications to various domains like medical diagnosis, motion detection and financial prediction, etc. Shapelet is probably one of the most commonly used approaches to tackle early classification problem, but one drawback of shaplet is its inefficiency. More importantly, the extracted shapelets may not be applicable to every test case at any time point. This work focuses on early classification of multivariate time series and proposes a novel framework named Multi-Domain Deep Neural Network (MDDNN), in which convolutional neural network (CNN) and long-short term memory (LSTM) are incorporated to learn feature representation and relationship embedding in the long sequences with long time lags. The proposed model can make predictions at any time point of a multivariate time series with the help of a truncation process. We conducted experiments on four real datasets and compared with state-of-the-art algorithms. The experimental results indicate that the proposed method outperforms the alternatives significantly on both of earliness and accuracy. Detailed analysis about the proposed model is also provided in this work. To the best of our knowledge, this is the first work that incorporates deep neural network methods (CNN and LSTM) and multi-domain approach to boost the problem of early classification on multivariate time series.