We will consider the elliptic relative equilibria of four-body problem with two small masses. The most interesting case is when the two small masses tends to the same Lagrangian point L4 (or L5). In 1991, Z. Xia showed that there exist four central configurations: two of them are non-convex, and the other two are convex. In the limiting case, we prove that the elliptic relative equilibria raised from the non-convex central configurations are always linearly unstable; while for the elliptic relative equilibria raised from the convex central configurations, the conditions of linear stable with respect to the parameters are given.
