Secondary electron emission (SEE) induced by interaction between positive ion and dielectric surface is essential physical process for maintaining sustained discharge and controlling the characteristics of atmospheric pressure dielectric barrier discharge (DBD). In this work, SEE is described based on Auger neutralization theory. Dielectric energy band structure and defect energy level, including hole and electron trap energy levels, are taken into account to build a hypothetical relationship γi = f (σ) between secondary electron emission coefficient γi and surface charge density σ. With the introduction of γi = f (σ) in DBD model, the characteristics of DBD are discussed in both first and steady discharges. It is found that, in steady discharge, γi has higher value during the beginning and development state of discharge pulse of DBD, and γi decreases in extinction stage. The negatively charged dielectric surface enhances SEE before discharge, which benefits the formation of diffuse discharge, compared with DBD of constant γi. Moreover, the increase of energy band gap of dielectric reduces γi, leading to the contractive discharge in DBD. The relationship between γi and σ can be further applied to study the influences of defect energy level parameters on SEE and DBD characteristics.