As a quantity characterizing the fluctuation of steps on vicinal surface, we study the step-position distribution function. This function gives the distribution of the position deviation of a step from the position equidistant from the two neighboring steps. On the basis of the harmonically-interacting step picture for vicinal surface, the relation between the step-position distribution function and the surface stiffness is obtained. The relation is verified by a Monte Carlo simulation for the free-Fermion terrace-step-kink (TSK) model and the solid-on-solid step TSK model.