The purpose of this study is to explore the process of inquiry problem finding in high school students' small group free-inquiry. For this purpose, 91 second grade high school students took part in small group free-inquiry. We conducted interviews with students (48 students in 15 groups) who were relatively successful in the inquiry performed for one semester (about 4 months). Based on the results of the interviews, we analyzed the characteristics of the inquiry problem finding through the steps and strategies in the inquiry problem finding process. The main results are as follows: First, in the inquiry problem finding process, steps such as selecting keyword, presenting an inconvenience, presenting a question, and finding an inquiry problem were found, and in particular, the process of selecting the keyword that correspond to the subject of inquiry, such as the material and situation of inquiry, is very important step in inquiry problem finding. Second, the strategies that students used in the process of finding inquiry problem included searching information, review of prior research, sharing of knowledge and experience, linking and extension of knowledge and experience, environmental awareness, expert consultation, discussion of suitability, elaboration, etc. Third, finding an inquiry problem was relatively easy in the inquiry for finding out problems (i.e. inconvenience) in everyday life and investigating ways to solve them. Fourth, the review of prior researches through the internet was useful in the process of selecting keyword and elaboration. Fifth, the factors that students consider when selecting one of several candidate inquiry problems are feasibility, real-life applicability, and economic condition. Sixth, the current affairs had a positive impact on the inquiry problem finding. Based on the above results, we discussed some ways to increase students' inquiry problem finding ability.