In this paper, we consider the elliptic relative equilibria of the restricted 4-body problems, where the three primaries form an Euler collinear configuration and the four bodies span R 2 . We obtain the symplectic reduction to the general restricted N -body problem. By analyzing the relationship between this restricted 4-body problems and the elliptic Lagrangian solutions, we obtain the linear stability of the restricted 4-body problem by the ω-Maslov index. Via numerical computations, we also obtain conditions of the stability on the mass parameters for the symmetric cases.