In this paper, we propose the use of center manifold theory to compute periodic orbits in the restricted three body problem such as halo, quasi-halo, horizontal and vertical Lyapunov orbits that attract much attention to conduct space observations missions. The proposed computation is simpler and easier to implement than existing methods such as Richardson's analytic construction method of periodic orbits or Poincare section method for finding quasi-periodic orbits since the proposed method simply integrates ordinary differential equations iteratively. The method also reveals the geometric structure of periodic orbits around the libration points.