Precursor continuous silicon carbide (SiC) fiber has a wide application prospect in the fields of aviation, aerospace and nuclear energy. The oxidation behavior and kinetics data of SiC fiber in a high-temperature oxidation environment are rather important for the research of composites. This review summarized the research work on continuous SiC fiber by a precursor method, oxidation type, performance degradation mechanism, oxidation process and oxidation kinetics of SiC fiber, and put forward the future research directions on oxidation behavior of SiC fiber.