We propose a new approach for extracting argument structure from natural language texts that contain an underlying argument. Our approach comprises of two phases: Score Assignment and Structure Prediction. The Score Assignment phase trains models to classify relations between argument units (Support, Attack or Neutral). To that end, different training strategies have been explored. We identify different linguistic and lexical features for training the classifiers. Through ablation study, we observe that our novel use of word-embedding features is most effective for this task. The Structure Prediction phase makes use of the scores from the Score Assignment phase to arrive at the optimal structure. We perform experiments on three argumentation datasets, namely, AraucariaDB, Debatepedia and Wikipedia. We also propose two baselines and observe that the proposed approach outperforms baseline systems for the final task of Structure Prediction.