The concept of function is the first important and difficult knowledge that high school students encounter when learning mathematics. The purpose of this study was to examine the understanding of the concept of function among freshmen at a senior high school in Inner Mongolia, China. This study adopted a combination of a questionnaire and a test concerning the concept of function in senior high school. The results show that freshmen have the following problems in the understanding of function concepts: understanding of the correspondence definition of function concepts is not thorough enough, the understanding of the concept and interrelationship of the three elements of functions is not deep enough, and there are major problems in understanding whether two functions are the same function, the graphics, and domain of abstract functions. Finally, provide suggestions to mathematics textbook writers to improve the content of function concepts.