Social contexts play important roles in the conversations.  The speakers need to always refer to those contexts when conversing.  Moreover, conversations do not only contain literal meanings but also meanings beyond the utterances.  This study therefore aims to reveal the social contexts that influence how the participants talk and produce conversational implicatures in the conversations, particularly among family members.  Four participants are involved with this study.  They are a father, mother, son and daughter from one family.  The data are taken from the conversations that occur only before school and father’s work using recording and note taking.  This study shows that the conversation among those four participants is rich of conversational implicatures.  There are several types of conversational implicatures found in this study.  Those are standard implicature with the highest emergence, particularized conversational implicature, generalized conversational implicature, and a deliberate flouting of the maxims.  This study concludes that the use of conversational implicature is strongly influenced by the social contexts of the participants, such as age, power or social status and social distance.