Keyword: low-dimensional quantum spin system, geometrical frustration, magnetic long-range order, field induced phase transition, charge transfer insulator.PACS Numbers: 75.10.Jm, 75.30.Kz, Abstract: We found new two-dimensional (2D) quantum (S=1/2) antiferromagnetic systems: CuRE2Ge2O8 (RE=Y and La).According to our analysis of high-resolution X-ray and neutron diffraction experiments, the Cu-network of CuRE2Ge2O8 (RE=Y and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular b-axis. Our bulk characterizations from 0.08 to 400 K show that they undergo a long-range order at 0.51(1) and 1.09(4) K for the Y and La systems, respectively. Interestingly, they also exhibit field induced phase transitions. For theoretical understanding, we carried out the density functional theory (DFT) band calculations to find that they are typical charge-transfer-type insulators with a gap of Eg ≅ 2 eV. Taken together, our observations make CuRE2Ge2O8 (RE=Y and La) additional examples of low-dimensional quantum spin triangular antiferromagnets with the lowtemperature magnetic ordering.