The longitudinal spin Seebeck effect has been investigated for a uniaxial antiferromagnetic insulator Cr2O3, characterized by a spin-flop transition under magnetic field along the c axis. We have found that a temperature gradient applied normal to the Cr2O3/Pt interface induces inverse spin Hall voltage of spincurrent origin in Pt, whose magnitude turns out to be always proportional to magnetization in Cr2O3. The possible contribution of the anomalous Nernst effect is confirmed to be negligibly small. The above results establish that an antiferromagnetic spin wave can be an effective carrier of spin current.