We have investigated the microwave nonreciprocity for a noncentrosymmetric antiferromagnet Ba2MnGe2O7. The magnon modes expected by the conventional spin wave theory for staggered antiferromagnets are certainly observed. The magnitudes of exchange interaction and magnetic anisotropy are obtained by the comparison with the theory. The microwave nonreciprocity is identified for one of these modes. The relative magnitude of microwave nonreciprocity can be explained with the use of spin wave theory and Kubo formula.