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 \pm 0.07 ) / t ^ { 3 } during the RD era and n ( t ) \simeq ( 0.25 \pm 0.05 ) / 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 .