The tokamak pedestal density structure is generally studied using a diffusion-dominant model. Recent investigations (Stacey and Groebner 2009 Phys. Plasmas16 102504) from first principle based physics have shown a plausible existence of large inward convection in the pedestal region. The diffusion–convection equation with rapidly varying convection and diffusion coefficients in the near edge region and model puffing–recycling neutral particles is studied in this paper. A peculiar property of its solution for the existence of the large convection case is that the pedestal width of the density profile, qualitatively different from the diffusion-dominant case, depends mainly on the width of the inward convection and only weakly on the neutral penetration length and its injection position.