English, as a communication tool, plays an extremely significant role in cross-cultural communication. While it is true that language users can mean exactly what they mean in their utterances, it is also true that they can have their utterances mean much more than what they say. Speakers of English speak indirectly, and using conversational implicatures is a way to be indirect. And as sentences often express messages above and beyond their literal meanings, it is not surprising that pragmatic errors are found in language learning process of EFL learners' communication. Therefore, this study aims at investigating the factors beyond misunderstanding or understanding of English conversational implicatures among Yemeni EFL university learners. It follows an empirical analytical-descriptive method consisting of a test and an interview. Randomly, 50% of the study population was selected as the study sample. They were 62 Yemeni EFL university learners. A multiple-choice discourse completion test ( MCDCT ) and a semi structure interview were used for collecting the study data. The test contained eleven types of conversational implicature The collected data was analyzed quantitatively and qualitatively. The results reveal that different factors caused misinterpretation of conversational implicatures among Yemeni EFL learners. However, the differences in socio-cultural knowledge and indirectness are instrumental in the misunderstanding of conversational contexts in the study. While the familiarity of some conversational implicatures and formulaic pattern of others pose no challenge for the study subjects to interpret some of the test conversational implicatures. The study test conversational implicatures that are formulaic or familiar to the subjects are easy to grasp. Therefore, this study provides some recommendations that are expected to enable EFL university learners to develop their pragmatic competence regarding English conversational implicature and suggests a reconsideration of the existing methodologies on teaching English as a foreign language. Hence, this would ease the concern of EFL students about English conversational implicature, build up their confidence and enhance language learning.