Teaching early warning is of great significance for avoiding teaching risks and continuously improving teaching quality. However, none of existing approaches assess the degree of course goals attainment and teacher's teaching quality from the perspective of cognitive diagnosis. This poses a challenge in providing accurate teaching early warning. This paper proposed an early warning approach for teachers based on cognitive diagnosis and long short-term memory (LSTM). First, this approach accurately evaluates students' cognitive status on knowledge concepts using a cognitive diagnosis model to assess their knowledge understanding degree and knowledge application ability. Second, the cognitive status on knowledge concepts is utilized to assess students' attainment degree of course goals and teachers' teaching quality. Third, the teachers' teaching quality is predicted in the future by using the LSTM network to mine students' learning process data, Finally, an accurate teaching early warning is provided to teachers based on a four-level early warning evaluation rule. In experiments, the real datasets are used and the results reveal that the proposed approach can accurately diagnose students' cognitive status and effectively predict teachers' teaching quality. This approach can provide an accurate teaching early warning service for teachers.