Despite advancements in vehicle security systems, over the last decade, auto-theft rates have increased, and cyber-security attacks on internet-connected and autonomous vehicles are becoming a new threat. In this paper, a deep learning model is proposed, which can identify drivers from their driving behaviors based on vehicle telematics data. The proposed Long-Short-Term-Memory (LSTM) model predicts the identity of the driver based on the individual's unique driving patterns learned from the vehicle telematics data. Given the telematics is time-series data, the problem is formulated as a time series prediction task to exploit the embedded sequential information. The performance of the proposed approach is evaluated on three naturalistic driving datasets, which gives high accuracy prediction results. The robustness of the model on noisy and anomalous data that is usually caused by sensor defects or environmental factors is also investigated. Results show that the proposed model prediction accuracy remains satisfactory and outperforms the other approaches despite the extent of anomalies and noise-induced in the data.