Mineral oil, as an insulating medium and coolant, has been used in core power equipment such as power transformer for more than 100 years. Compared with mineral oil and other ester liquids, natural ester insulating oil has higher flash point, biodegradation and better electrical performance, which has a wide application prospect. However, the research on the discharge characteristics and fault criteria of natural ester insulating oil are very limited. In this paper, the gas production characteristics of three kinds of natural ester insulating oil (FR3, RAPO and RDB) and mineral oil under partial discharge along surface were studied and compared. The simulation results of the electrode of weak vertical component surface discharge show that the quarter spherical electrode generates more ideal electric fields than the needle electrode does. The dissolved gases generated in the surface discharge dominated by the vertical electric field, mainly consist of hydrogen, ethane, and acetylene, while the main dissolved gases are hydrogen and ethane when the discharge is dominated by the parallel electric field. The production characteristics of acetylene in esters is significantly different from mineral oil under partial discharge. The IEC ratio method is not suitable for the fault judgement of natural esters. The research is expected to provide a reference for the development of the new detection methods of dissolved gas analysis (DGA) and failure criterion.