As high-performance, eco-friendly thermosetting resins progress, research on recyclable and reprocessable epoxy resins is on the rise. Epoxy resin cured with anhydride is a typical insulating material used in electrical equipment due to its advantages, such as good dimensional stability, resistance to cracking, excellent electrical insulation, and superior mechanical properties. However, its stable three-dimensional cross-linked network structure is difficult to recycle and degrade. The solid waste generated by decommissioning not only causes waste of resources, but also causes serious environmental pollution. In order to solve the above problems, researchers have utilized dynamic covalent bonds to construct highly active dynamic crosslinked networks, which is a key way to endow epoxy resin with recycling and degradation properties. In this study, two kinds of epoxy vitrimers based on dynamic ester bonds were prepared by using 1,5,7-triazabicyclo [4.4.0] dec-5-ene (TBD) and thermal latent catalyst MY-24 as catalysts on the basis of trifunctional epoxy resin (AFG-90). The effects of two catalysts on the curing process of epoxy vitrimers were systematically analyzed by non-isothermal differential scanning calorimetry (DSC). The curing kinetic model was established and the theoretical curing temperature was determined. The results show that the epoxy vitrimer system with different catalysts conforms to the autocatalytic two-parameter curing kinetic model, and the curing temperature decreases with the increase of catalyst content. The curing kinetics model is used to determine the optimal curing process system, which provides experience and guidance for the epoxy resin curing process of environmentally friendly dry-type transformers.