A two-dimensional full Fokker-Planck (FP) simulation code coupled with an ideal fluid equation has been constructed. This code was applied for the numerical simulation of the Rayleigh-Taylor (RT) instability on the directly driven ablation front. The simulation results show that an accelerated thin foil is preheated by the non-local electron heat transport, the ablation front density is depleted, and the linear growth rate of the RT instability is suppressed strongly. By investigating the mode structure in the simulation, it is found that the peak of the eigen mode shifts toward the corona region by the non-local heat conduction effects. This is the reason why the growth rate is reduced.