In this article, we perform the computation of halo orbits around libration point L1 in the Sun–Jupiter system. Third-order approximation, Lindstedt–Poincare method is used to select the initial guess for libration point orbits. Furthermore, Newton’s differential correction scheme is utilized to correct the initial guess obtained from an analytical approach. Halo orbits are exceptionally unstable, the station-keeping maneuver is required to maintain the nominal halo orbit in the vicinity of collinear libration points. We have applied linear control logic in the non-linear equation of motion for the station-keeping error analysis of halo orbits and also computed the control input for halo orbits. Numerical results illustrate the viability of the proposed control technique for the exact station-keeping error at libration point L1.