The classically balanced facility location problems aim to find the location of one or several new facilities such that some balanced function is optimized. This paper concerns the problem of improving the balanced objective at a prespecified vertex of a tree as much as possible within a given budget. We call such a problem the reverse selective balance center location problem on trees. All vertices are partitioned into two disjoint sets, in which one set consists of selective vertices. The balanced function is considered to be the difference in distance between the furthest demand point in the selective set and the nearest one in the remaining set. We first formulate the problem as linear programming. Then we propose a strategy to reduce the objective value in the case of variable edge lengths. An algorithm is developed to solve the reverse selective balance center location problem on trees in quadratic time.