Photovoltaic performances of Cu-chalcogenides solar cells are strongly correlated with the absorber fundamental properties such as optimal bandgap, desired band alignment with window material, and high photon absorption ability. According to these criteria, we carry out a successive screening for 90 Cu-chalcogenides using efficient theoretical approaches. Besides the well-recognized CuInSe2 and Cu2ZnSnSe4 materials, several novel candidates are identified to have optimal bandgaps of around 1.0-1.5 eV, spike-like band alignments with CdS window layer, sharp photon absorption edges, and high absorption coefficients. These new systems have great potential to be superior absorbers for photovolatic applications if their carrrier transport and defect properties are properly optimized.