Feature selection is the process of selecting a subset of features that provides maximum of the information, present otherwise in entire dataset. The process is very helpful when input for different tasks including classification, clustering, rule extraction and many others, is large. Rough Set Theory, right from its emergence, has been widely used for feature selection due to its analysis friendly nature. Various approaches exist in literature for this purpose. However, majority of them are computationally too expensive and suffer a significant performance bottleneck. In this paper we have proposed a new feature selection approach based on rough set theory, using random feature vector generation method. The proposed approach is a two steps method. At first, it generates a random feature vector and verifies its suitability for being a potential candidate solution. If it fulfills the criteria, it is selected and optimized, otherwise a new subset is formed. The proposed approach was verified using five publicly available datasets. Results have shown that proposed approach is computationally more efficient and produces optimal results.