In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqueness of the solution of the problem are presented, and error bounds $O(h^{\frac{3}{4}})$ and $O(h^{\frac{3}{2}})$ are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for $k=0$ and $k=1$ respectively.