The binary population in field stars and star clusters contributes to the formation of gravitational wave (GW) sources. However, the fraction of compact-object binaries (CBs), which is an important feature parameter of binary populations, is still difficult to measure and very uncertain. This paper predicts the fractions of important CBs and semi-compact object binaries (SCBs) making use of an advanced stellar population synthesis technique. A comparison with the result of N-body simulation is also presented. It is found that most CBs are formed within about 500 Myr after the starburst. The fractions of CBs and SCBs are demonstrated to correlate with stellar metallicity. The higher the metallicity becomes, the smaller the fraction of black hole binaries (BHBs), neutron star binaries (NSBs) and SCBs. This suggests that the GW sources of BHBs and NSBs are more likely to form in metal-poor environments. However, the fraction of black hole-neutron star binaries is shown to be larger for metal-rich populations on average.