Zn1-xMgxO (ZMO) second buffer was applied to replace conventional ZnO second buffer layer of Cu-2(Sn,Ge)S-3 (CTGS) solar cells to reduce interface carrier recombination and open-circuit voltage deficit (V-OC,V-def). Structure of the solar cell is glass/Mo/CTGS/CdS first buffer/ZMO second buffer/ZnO:Al (AZO)/Ni-Al. Bandgap energy (E-g) of the ZMO films is changed from 3.20 to 3.65 eV by varying Mg/(Mg + Zn) ratio from 0 (for pure ZnO) to 0.26. The increase in the Eg of ZMO films is attributable to the move of conduction band minimum (E-C). It is determined that ZMO second buffer with increase in E-g from 3.20 to 3.55 eV yields the smoothing conduction band offset (CBO) at ZMO/CdS interface varying from -0.26 to +0.09 eV. Saturation current density (J(0)) is therefore reduced to the lowest value, and activation energy of recombination (E-A) is the closet to the E-g of the CTGS absorber layer, implying the lowest interface carrier recombination (reduced V-OC,V-def), and thereby increasing conversion efficiency (eta) to 4.5% (E-g of ZMO: 3.55 eV). On the other hand, the ZMO second buffer with E-g larger than 3.55 eV results in the CBO at ZMO/CdS interface of +0.19 eV (E-g of ZMO: 3.65 eV), making the well of E-C structure in ZMO/CdS/CTGS stacking layers, thus increasing interface carrier recombination, and severely decreasing the eta to about 0.2%.