The surface polarization energy that arises from the difference in dielectric coefficient between the quantum dot (QD) and the background medium is investigated by the equivalent image charge method. A general expression for the bandgap of QD depending on the dielectric coefficient of background medium is presented by solving the exciton Schrödinger equation with the perturbation method. As examples, the sizedependent bandgaps, bandgap shifts, absorption-peak wavelengths and absorption-peakwavelength shifts of PbSe, PbS and CdSe QDs doped in different background media are determined in detail. There is evidence to show that the effects of surface polarization on the bandgap and the first absorption-peak wavelength of QD are considerable. The bandgap decreases with the increase of dielectric coefficient of background medium, which causes the absorption-peak wavelength to be red shifted. The effect of surface polarization on the bandgap depends substantially on the sign and value of image charge. When the dielectric coefficient of QD is greater than that of background medium, the absorption-peak wavelength comes to blue shift due to surface polarization of QD. On the contrary, the absorption-peak wavelength comes to redshift. The absorption-peak wavelength shifts of QDs doped in different background media will reach a maximum in a certain diameter depending on the kind of QD.