A conversion efficiency (Eff) of 5.83% on a Cd-free Cu2ZnSnS4 (CZTS) thin-film solar cell is achieved with a chemical bath deposited Zn-based buffer layer instead of the more commonly used but toxic Cd-based buffer layer. Vacuum-based techniques are used for the other processes. In this work, we focus on the applicability of the Zn-based buffer with CZTS absorbers of various compositions. Relationships between the electrical parameters of the Zn-based buffer cells and Zn/Sn ratio of the absorbers show interesting behaviors. In the case of the low Zn/Sn ratio, such as around 1.0, the Zn-based buffer cells have higher Eff than the Cd-based buffer cells. However, when the Zn/Sn ratio is increased, only the Zn-based buffer cells show strong degradation in Eff due to the deterioration of both the open circuit voltage and the fill factor. These results clearly show that there is a strong relationship between the applicability of the Zn-based buffer and the composition of the CZTS absorber.