This paper proposes a method for handling out-of-vocabulary (OOV) words that cannot be translated using conventional phrase-based statistical machine translation (SMT) systems. For a given OOV word, lexical approximation techniques are utilized to identify spelling and inflectional word variants that occur in the training data. All OOV words in the source sentence are then replaced with appropriate word variants found in the training corpus, thus reducing the number of OOV words in the input. Moreover, in order to increase the coverage of such word translations, the SMT translation model is extended by adding new phrase translations for all source language words that do not have a single-word entry in the original phrase-table but only appear in the context of larger phrases. The effectiveness of the proposed methods is investigated for the translation of Hindi to English, Chinese, and Japanese.