The aim of this study is to explain implication occurring in conversation and to suggest the orientation of its teaching. Today, specially learning of speaking-listening in Korean language education follows Grice`s 4 maxims as important rules. Grice described these expectations in terms of a Co-operative Principle and maxims of Quality (truthfulness), Quantity (informativeness), Relation (relevance) and Manner (clarity) which speakers are expected to observe(Grice 1961). But Grice`s theories have the meaning to explain the implications when they very often occur in everyday-conversation. The interpretation a rational hearer should choose is the one that best satisfies those expectations. The goal of inferential pragmatics is to explain how the hearer infers the speaker`s meaning on the basis of the evidence provided. And implication theory is connected with Sperber & Wilson`s the relevance theories. They share Grice`s intuition that utterances raise expectations of relevance, including the need for a Co-operative Principle and maxims, the focus on pragmatic processes which contribute to implicatures rather than to explicit, truth-conditional content, and the treatment of figurative utterances as deviations from a maxim or convention of truthfulness. In the education of conversation, it is important that students know maxims as the mechanism of implication but in itself.