In this paper, under effects of the largest primary radiation pressure the elliptic restricted Four-Body Problem is formulated in Hamiltonian form, the canonical equations are obtained which are considered as the equations of motion. The Lagrangian points within the frame of the elliptic restricted four-body problem are obtained. The true anomalies are considered as independent variables. An analytical and numerical approach had been used. A code of Mathematica is constructed to truncate these considerations and is applied on the Earth-Moon-Sun system. The stability and periodicity of the motion about the equilibrium points are studied by using the Poincare maps, The motion about the collinear points L2 is presented as an example for the obtained results, and some families of periodic orbits are presented.