In inertial confinement fusion (ICF), electron thermal transport plays a key role in the laser ablation and subsequent implosion processes, which, however, always exhibits the intractable non-local effect. Simple modifications of the local Spitzer-Härm model with either an artificially-assumed constant flux limiter or a purely time-dependent one are applied to explain some experimental data, but fails to simultaneously reproduce the space-time evolution of the whole laser ablation process. Here, through carrying out a series of one-dimensional and two-dimensional radiation hydrodynamic simulations, where the space-time-dependent non-local thermal transport model proposed by Schurt, Nicolaı̈ and Busquet (the SNB model) are self-consistently included, we systematically study the non-local effects on the whole laser ablation dynamics including those occurring at the critical surface, the conduction zone and the ablation front. Different from those obtained previously, our results show that, because of the non-local heat flow redistribution and redirection, at the critical surface the thermal flux is more inhibited, in the conduction zone the lateral thermal transport is suppressed, and ahead of the ablation front the plasma is preheated, which, combined together, eventually result in significant improvement of the laser absorption efficiency, extension of the conduction zone, increase of both the mass ablation rate and shock velocity. Furthermore, dependences of these laser ablation dynamics on different drive laser intensities are investigated, which provides beneficial enlightenments on potential laser pulse shaping and/or ignition scheme optimization in ICF.