A lattice self-avoiding polymer chain with one end attached to an adsorbing flat surface is simulated using Monte Carlo method. The chain model has z = 26 bond vectors with bond length being 1, root 2, and root 3 on the simple cubic lattice. The dependence of the number of surface contacts M on temperature T in the unit E/k(B) with E the interacting energy and k(B) the Boltzmann constant and chain length N is investigated by a finite-size scaling law M = N-phi(a(0) + a(1)(T - T-c)N-1/delta + O((T - T-c)N-2(2/delta))) near the critical adsorption point T-c. It was estimated that T-c = 1.625 and the exponents phi = 0.52 and d = 1.63. It was observed that both mean square end-to-end distance < R-2 > and mean square radius of gyration < R-g(2)> reach minimum at T-c. And we discover that the asphericity parameter < A > is independent of chain length at T-c. A simple relationship is discovered between T-c and bond vector number n(b) for lattice chain models, and which can be extended to nonlattice chain models by introducing an attraction range fraction f. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012