This paper addresses the problem of Twitter sentiment analysis through a hybrid approach in which SentiWordNet (SWN)-based feature vector acts as input to the classification model Support Vector Machine. Our main focus is to handle lexical modifier negation during SWN score calculation for the improvement of classification performance. Thus, we present naive and novel shift approach in which negation acts as both sentiment-bearing word and modifier, and then we shift the score of words from SWN based on their contextual semantic, inferred from neighbouring words. Additionally, we augment negation accounting procedure with a few heuristics for handling the cases in which negation presence does not necessarily mean negation. Experimental results show that the contextual-based SWN feature vector obtained through shift polarity approach alone led to an improved Twitter sentiment analysis system that outperforms the traditional reverse polarity approach by 2–6%. We validate the effectiveness of our hybrid approach considering negation on benchmark Twitter corpus from SemEval-2013 Task 2 competition.