The main purpose of this study is to investigate eighth-grade students¡¦ understanding of the equal sign and analyzed error types of quadratic equation in one variable. To achieve this purpose, the investigator did a survey and development instruments. Participants were 215 eighth-grade students who formed a convenient sample. There are three results. First, participants with a relational definition of the equal sign added to about 80% of the sample. Second, the performance of students with relational definitions is higher than the performance of students with operational definitions. Third, students¡¦ understanding of the equal sign was related to their respective problem-solving performance on quadratic equation in one variable. In this study, participants with an operational definition of the equal sign tended to guess randomly or leave a blank. Problem-solving performance of participants with a relational definition of the equal sign involved multiple strategies. The researcher suggested that teachers should strengthen students¡¦ understanding of equal sign and related students¡¦ prior algebraic knowledge.