In 1985, Perko, L.M. and Walter, E.L. [1] proved that N (N ≥4) bodies located at the vertices of a regular polygon form a central configuration if and only if all bodies have the same mass. In 2018, Chen, J. and Luo, J. [2] proved that the configuration which N (N ≥3) bodies are at the vertices of a regular polygon with the N+1-th body located at the center of the polygon is a central configuration if and only if the former N bodies have the same mass. In this paper, we proved that N (N ≥3) infinitesimal bodies located at the vertices of a regular polygon with a dominant body located at the center of the polygon form a central configuration of the planar 1+N -body problem if and only if the masses of all the infinitesimal bodies are equal when N is odd and the masses of the alternate infinitesimal bodies are equal when N is even.