We perform population synthesis simulations for Population III (Pop III) coalescing compact binary which merges within the age of the Universe. We found that the typical mass of Pop III binary black holes (BH–BHs) is ∼30 M⊙ so that the inspiral chirp signal of gravitational waves can be detected up to z = 0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH–BHs is $140(68)\ {\rm events\,yr^{-1} \,(SFR_p/(10^{-2.5}\,{\rm M}_{\odot }\,yr^{-1}\,Mpc^{-3}))\cdot Err_{sys}}$ for the flat (Salpeter) initial mass function, respectively, where SFRp and Errsys are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. Errsys = 1 corresponds to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH–BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by the Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH–BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass ∼30 M⊙ by the detections of gravitational waves if the merger rate of the Pop III massive BH–BHs dominates that of Pop I BH–BHs.