In the post epidemic era, the online offline mixed teaching mode is in the development period, and college teachers and students are gradually familiar with this teaching mode. Taking the course introduction to petrochemical equipment management as an example, this paper deeply analyzes the development path of online offline mixed teaching mode. First of all, this paper explores the bottleneck of online teaching in the epidemic era, deeply analyzes the relationship between online teaching and offline teaching, and puts forward the possibility of integration of offline teaching and online teaching. Based on the above analysis results, this paper summarizes the opportunities of Blended Teaching in the post epidemic era. This paper puts forward the practice path of the online and offline mixed teaching mode of “Introduction to petrochemical equipment management”. Finally, the online and offline mixed teaching quality evaluation model of “Introduction to petrochemical equipment management” is constructed, the mixed teaching quality evaluation index system is determined, and the evaluation model based on improved firefly algorithm optimization fuzzy neural network is constructed, and the example analysis is carried out, and the online and offline mixed teaching quality of “Introduction to petrochemical equipment management” is determined as good, It provides a favorable theoretical basis for the reform strategy of mixed teaching mode, and also verifies the effectiveness of the evaluation model.