The size and the shape of non-reversal random-walking polymer chains near an impenetrable, non-interacting flat surface are investigated by means of Monte Carlo simulation on the simple cubic lattice. It was found that both size and shape are dependent on the normal-to-surface distance z(o) of the first segment of chain. We find that the size and shape of chains, characterized by mean square radius of gyration(S-2) and mean asphericity parameter (A) respectively, show similar dependence on distance z(o). Both (S-2) and (A) reach the maximum at z(o) = 0, then decrease with the increase of z(o) and soon reach the minimum values, afterwards they go up continuously and approach to the limit values of free chain. The similar dependence of (S-2) and (A) on z(o) can be explained by a positive correlation between A and S-2. However, the dependence of the correlation coefficient C-A,(S2) on z(o) is very complicated and deserves further study. The overall density probability of segments is also investigated. Results show that segments near the surface are relatively less, and the symmetrical distribution disappears when the chain locates near the surface.