Here, we report Cu2S nanocrystals based non-fullerene ternary polymer solar cells by incorporating Cu2S in conjugated polymer (PBDB-T: poly [(2,6-(4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)-benzo[1,2-b:4,5-b']dithiophene))-alt-(5,5 (1',3'-di-2-thienyl-5',7'-bis(2-ethylhexyl) benzo[1',2'-c:4',5'-c']dithiophene-4,8-dione))]) and small molecule non-fullerene compound (ITIC:3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2',3' d']-s-indaceno[1,2-b:5,6-b]dithiophene). The devices were fabricated in inverted configuration i.e. ITO/ZnO/PBDB-T: Cu2S NCs: ITIC/MoO3/Ag. Effect of concentration of Cu2S nanocrystals on the performance parameters of PBDB-T: ITIC based organic solar cells is studied. An enhancement in the power conversion efficiency from 8.24% to 9.53% is achieved for the optimum concentration of Cu2S nanocrystals in the organic photoactive blend. The cause of improvement in the performance parameters of the device is investigated by means of the light intensity dependent electrochemical impedance spectroscopy and atomic force microscopy. It is found that the devices with Cu2S nanocrystals have less trap-assisted recombination.