Twitter is the largest and most popular micro-blogging website on Internet. Due to low publication barrier, anonymity and wide penetration, Twitter has become an easy target or platform for extremists to disseminate their ideologies and opinions by posting hate and extremism promoting tweets. Millions of tweets are posted on Twitter everyday and it is practically impossible for Twitter moderators or an intelligence and security analyst to manually identify such tweets, users and communities. However, automatic classification of tweets into pre-defined categories is a non-trivial problem problem due to short text of the tweet (the maximum length of a tweet can be 140 characters) and noisy content (incorrect grammar, spelling mistakes, presence of standard and non-standard abbreviations and slang). We frame the problem of hate and extremism promoting tweet detection as a one-class or unary-class categorization problem by learning a statistical model from a training set containing only the objects of one class . We propose several linguistic features such as presence of war, religious, negative emotions and offensive terms to discriminate hate and extremism promoting tweets from other tweets. We employ a single-class SVM and KNN algorithm for one-class classification task. We conduct a case-study on Jihad, perform a characterization study of the tweets and measure the precision and recall of the machine-learning based classifier. Experimental results on large and real-world dataset demonstrate that the proposed approach is effective with F-score of 0.60 and 0.83 for the KNN and SVM classifier respectively.