The secondary-electron emission (SEE) coefficient, delta, was measured for thermally grown SiO2 films on a Si wafer. As the thickness of SiO2, film becomes greater than 40 similar to 50 nm, the SEE curve changes to the double-humped shape having a low 8 value from the typical 'universal curve' shown at ordinary SEE measurements. We conclude, from a comparison of the SiO2 thickness and the penetration depth of primary electrons, that this is due to the surface charging effect of all insulating SiO2 film. To overcome the charging effect, an electric field is introduced inside a thick SiO2 film (55 nm) by applying a negative bias potential to the sample. When the bias potential is increased, delta of thick SiO2 is increases constantly up to value similar to that for thin SiO2 (2 nm), and the SEE curve recovers the original, universal curve form. The role of the bias potential is believed to increase the tunneling probability between the bulk Si and the SiO2 surface, and thus electrons from Si call easily be supplied to the SiO2 surface, where holes are generated upon the departure of secondary electrons.