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Driver's anxiety about the remaining driving range of electric vehicles (EVs) has been quite improved by mounting a high-capacity battery pack. However, when EVs need to be charged, the drivers still feel uncomfortable if inaccurate range prediction is provided because the inaccuracy makes it difficult to decide when and where to charge EV. In this paper, to mitigate the EV range anxiety, a new machine learning (ML) method to enhance range prediction accuracy is proposed in a practical way. For continuously obtaining the recent traffic conditions ahead, input features indicating the near-future vehicle dynamics are connected to a long short-term memory (LSTM) network, which can consecutively utilize a relation of neighboring data, and then the output features of the LSTM network with another input features consisting of energy-related vehicle system states become another input layer for deep learning network (DNN). The proposed LSTM-DNN mixture model is trained by exploiting the driving data of about 160,000 km and the following test performance shows that the model retains the range prediction accuracy of 2 ~ 3 km in a time window of 40 min. The test results indicate that the LSTM-DNN range prediction model is able to make a far-sighted range prediction while considering varying map and traffic information to a destination.