Cold atom physics in space station attract a lot of interest of scientists. We investigate the dynamical output process of the space continuous atom laser by solving non-linear Gross-Pitaevksii equations numerically. Slow-moving continuous atom beams in two directions are observed simultaneously. The slow-moving coherent atom beams can be used as a source of atom interferometer to do long-time measurements. We also control the output of space atom laser by adjusting the output coupling strength.