In this paper, we propose a general Poisson-Boltzmann model for electric double layer (EDL) analysis with the position dependence of dielectric permittivity considered. This model provides physically reasonable property profiles in the EDL region, and it is then utilized to investigate the depletion layer effect on EDL structure and interaction near hydrophobic surfaces. Our results show that both the electric potential and the interaction pressure between surfaces decrease due to the lower permittivity in the depletion layer. The reduction becomes more profound at larger variation magnitude and range. This trend is in general agreement with that observed from the previous stepwise model; however, that model has overestimated the influence of permittivity variation effect. For the thin depletion layer and the relative thick EDL, our calculation indicates that the permittivity variation effect on EDL usually can be neglected. Furthermore, our model can be readily extended to study the permittivity variation in EDL due to ion accumulation and hydration in the EDL region.