This paper studies the vector optimization problem of finding weakly ef- ficient points for maps from Rn to Rm, with respect to the partial order induced by a closed, convex, and pointed cone C ⊂ Rm, with nonempty inte- rior. We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem with a modified convergence sensing conditon that allows us to construct an interior proximal method for solving POV on nonpolyhedral set.