  In this paper, we study the motion of test particle and light around the
Global Monopole in asymptotically dS/AdS spacetime. The motion of a test
particle and light in the exterior region of the global monopole in dS/AdS
spacetime has been investigated. Although the test particle's motion is quite
different from the case in asymptotically flat spacetime, the behaviors of
light(null geodesic) remain unchanged except a energy(frequency) shift. Through
a phase-plane analysis, we prove analytically that the existence of a periodic
solution to the equation of motion for a test particle will not be altered by
the presence of cosmological constant and the deficit angle, whose presence
only affects the position and type of the critical point on the phase plane. We
also show that the apparent capture section of the global monopole in dS/AdS
spacetime is quite different from that in flat spacetime.
