We study statistical thermodynamical behavior of the vicinal surface with adsorption. We consider the case where attractive lateral interactions between adsorbates are present, which cause the thermal step bunching. As the microscopic model Hamiltonian for the vicinal surface with adsorption, we adopt a restricted-solid-on-solid model coupled with the Ising system. Using the density-matrix renormalization group algorithm, we obtain surface-free energy and adsorption coverage as functions of the surface slope p. We derive the step tension and the step-interaction coefficient from the free energy. We clarify the origin of the thermal step bunching and the adsorbate-mediated interstep attraction.