The binding energies of excitons in symmetrical GaAs/Al0.3Ga0.7As double quantum wells are calculated variationally by using a simple wave function within the effective-mass approximation. The variation of the binding energies as functions of the well and barrier width is studied. It is found that, the changing tendency of the binding energies with the well width is similar to that of the single quantum well. However, we found that the maximum value of the binding energy occurs at well size of about 10?. The well size is smaller than that in single quantum wells. The binding energies have a minimum during the increase of the barrier width, which is related to the penetration into the barrier of the wave function.