  We investigate the scaling property of global monopoles in the expanding
universe. By directly solving the equations of motion for scalar fields, we
follow the time development of the number density of global monopoles in the
radiation dominated (RD) universe and the matter dominated (MD) universe. It is
confirmed that the global monopole network relaxes into the scaling regime and
the number per hubble volume is a constant irrespective of the cosmic time. The
number density $n(t)$ of global monopoles is given by $n(t) \simeq
(0.43\pm0.07) / t^{3}$ during the RD era and $n(t) \simeq (0.25\pm0.05) /
t^{3}$ during the MD era. We also examine the peculiar velocity $v$ of global
monopoles. For this purpose, we establish a method to measure the peculiar
velocity by use of only the local quantities of the scalar fields. It is found
that $v \sim (1.0 \pm 0.3)$ during the RD era and $v \sim (0.8 \pm 0.3)$ during
the MD era. By use of it, a more accurate analytic estimate for the number
density of global monopoles is obtained.
