The purpose of this paper is to discuss contextual implicature based on relevance theory to make the importance of context underlying what is uttered clear. For this purpose we critically reviewed Grice`s approach to the conversational implicature. Then we compared and analysed the differences between Grice`s approach and the Theory of Relevance. We applied Sperber and Wilson`s theory of relevance and showed its adequacy by examining various kinds of examples. In conclusion, this paper has shown that theory of relevance is intended to explain ostensive communication as a whole, both explicit and implicit.