Mental models are one form of ideas in the minds of individuals that can be used to describe, explain and predict a particular phenomenon. The pre-initial form of individual mental models can be seen from information held by children stored in their long-term memory before they are confronted with a particular concept. The purpose of this study was to describe the characteristics of pre-initial mental models of first-grade students in understanding the concept of function. This study belongs to qualitative research with a case study design. The case that was observed in this study was the students' pre-initial mental model in understanding the concept of function. The researchers, then, set two subjects of each reason for the answers to be interviewed. To guarantee the validity and reliability of the research, the triangulation technique was employed by displaying the data yielded from the interview video and comparing it with the results of the students' written test. The results show that first-grade students who are at the level of pre-initial mental models do not understand the concept of relations well so that they are not able to solve the problem of relations that is not a function.