In this article we introduced the gravity observation system of Crustal Movement Observation Network of China(CMONOC). We studied the fractal characteristics of CMONOC gravity network from the perspective of fractal geometry,and calculated the fractal dimension of gravity network as D_f=1.5598,with the optimal grid spacing r=139km. We made a comprehensive analysis on the fractal dimension,gravity time-varying distance,gravity anomaly range,and the survey network range in order to estimate the capability of earthquake monitoring of the CMONOC. The results show that the optimal grid spacing of the survey network is close to the radius of the characteristic anomaly area of the gravity field change area caused by the M_S6.0 earthquakes,and the CMONOC gravity network is capable of monitor earthquakes above M_S6.0 in continental China except for the regions at the border and no civilization area in northern Tibet.