In this paper, the impacts of boundary on the surface bright soliton in (1+1)-dimensional nonlocal nonlinear media are investigated First the solution of the surface soliton under the given boundary conditions in a normalized system is derived, and then, the critical power and the balance position of the surface soliton are obtained. Next, in the numerical simulation, due to the impact of boundary, it is difficult to form stable solitons when the width of the sample is too small. And the impact of the boundary on the soliton can be ignored only if the width of the sample is large enough; then the stable soliton can exist, which is similar to the analytical results. In addition, the impact of the boundary on the surface soliton when beams do not input from its equilibrium position is also investigated. In this case, the beam will propagate oscillating periodically about the stationary position, which is equivalent to the interaction of two out-of-phase solitons in nonlocal bulk media. Both the oscillating trajectory and period dovetail coinsde nicely with each other.