The multi-objective competitive location problem with distance-based attractiveness for two facilities (MOCLP-2 facilities) is introduced in this paper. A demand point is covered by two facilities, and the preferred facility satisfies the criteria of maximum attractiveness and minimum distance to the demand point. Facility attractiveness is defined as a distance-based coverage of the facility that can be full coverage, no coverage, or partial coverage of the demand point, depending on the within maximum full coverage radius, outside partial coverage radius between those two radii, respectively. The problem is formulated as a multi-objective optimization model to find a facility with maximum attractiveness and minimum distance. The contributions of this paper is that the problem can be tractably decided by the introduced non-dominated range (N.d. range) with less computation. Furthermore, extensive examples for facility selection and sensitivity analysis demonstrate its effectiveness and efficiency by the developed N.d. range.