The present study aims to suggest a concept of Grammar Inquiry Task as one of the most important prerequisites that facilitate Grammar Inquiry Learning in Korean Grammar Education and to conduct a preliminary investigation of the plausible design of the Grammar Inquiry Task. Grammar Inquiry Task defines the purpose, contents, and methods of learner`s inquiry activity and guides them. This concept embraces the formality and the contents and is a whole set of information that instruct the general outline of Grammar Inquiry Activity telling “What to choose”, “How to deal with”, and “What results to get”. Therefore, in order to facilitate educational Grammar Inquiry Activity a subtle and sophisticated design of teaching is required; especially all consideration must be given to Grammatical Thinking processes that are expected for the learners to perform. Items of International Linguistics Olympiad(ILO) are analyzed. Since these items are developed to test rational and creative metal activities of the test takers setting a language as an object of investigation, the rationale and elaboration of the items can fully support the concept of appropriate base line data of the present study to examine the direction of the design of Grammar Inquiry Task. The study analyzed the items of International Linguistics Olympiad(ILO) as a representative case of Grammar Inquiry Task and reviewed ‘what grammatical thinking process is presupposed in the inquiry task’ and ‘how the real thinking process is induced.’ The final part of the study presents basic principled foundation of Grammar Inquiry Task design that will expedite Grammatical Thinking and subtly adjust and guide the thinking process.