Natural-convective heat transfer of oscillating vertical plates is related to industrial and technological applications. In this paper, a numerical study is described of the laminar natural convection on a periodically oscillating vertical flat plate heated at a uniform temperature. The exact solutions for the classical Stoke's problem and the similarity solutions (by Ostrach) are used to verify the numerical formulation. Of particular interest of this paper is the heat transfer characteristics when the oscillatory velocity being close to the flow velocity in the velocity boundary layer under non-oscillation condition. The results show that a two-fold increase in space-time averaged Nusselt number is achieved. And it is found that the heat transfer for the problem under consideration significantly depends on the dimensionless oscillation velocity, a relative size between the oscillation velocity and the flow velocity in the velocity boundary layer of a stationary plate. The effects of the governing parameters on the heat transfer are investigated numerically. The heat transfer enhancement is found to be increased with the dimensionless oscillation frequency, amplitude, the Prandtl number, but decreased with the Grashof number. (C) 2004 Elsevier Ltd. All rights reserved.