The Nd permanent magnet (Nd2Fe14B) is an indispensable material used in modern energy conversion devices. The realization of high coercivity at finite temperatures is an important issue. One of the important ingredients for controlling the coercive force is the surface property of magnetic grains. It has been found by first-principles studies that the Nd atoms in the first (001) surface layer facing the vacuum have in-plane anisotropy perpendicular to the c axis, which may decrease the coercivity. Focusing on the surface anisotropy effect on the coercivity, we examine the coercivity at zero and finite temperatures using an atomistic model reflecting the lattice structure of the Nd magnet with a stochastic Landau-Lifshitz-Gilbert equation method. We study three general cases, in which the Nd atoms in surface layers have (1) no anisotropy, (2) in-plane anisotropy, and (3) reinforced anisotropy for two types of surface, (001) and (100) surfaces. We find that in contrast to the zero-temperature case, owing to the thermal fluctuation effect, the modification of only the first surface layer has little effect on the coercivity at finite temperatures. However, the modification of a few layers results in significant effects. We discuss the details of the dependences of the coercivity on temperature, the type of surface, and modified layer depth, and also the features of domain growth in magnetization reversal.