The Morales-Ramis theory has been applied to many Hamiltonian systems to prove the non-integrability. Especially Maciejewski and Przybylska proved that the three-body problem is not integrable by using the Morales-Ramis theory. In order to prove it, they studied the variational equations along the Euler and Lagrange homothetic solutions. In this talk, we will prove the non-integrability of the restricted n-body problem. It is more difficult, because there is no homothetic solution. We will focus on the singularity which the extended differential equations have, and then apply the Morales-Ramis theory to it.