For kesterite Cu2ZnSnSe4 (CZTSe) solar cells, the CZTSe absorber is usually fabricated using a two-step process, in which the CZTSe absorber is made by using post-selenization of a sputtered metal stack film. In the post-selenized CZTSe film, a rough surface, voids, and small-grained structures at bottom near the Mo back contact are frequently observed. To avoid these inferior features, we designed and fabricated a new modified stack layer that showed compact and larger grains with no voids and with small-grain-free near the bottom side. Several measurements, such as X-ray diffraction, Raman spectroscopy, photoluminescence, and time-resolved photoluminescence measurements, showed that the selenized film from the newly designed stack layer had high crystal quality. With the fabricated absorber, we made two types of CZTSe solar cells, one with a CdS buffer and the other with a (Zn,Sn)O buffer. The (Zn,Sn)O- buffered CZTSe solar cell showed a power conversion efficiency of 8.31%, which is comparable to the 8.84% of the CdS-buffered CZTSe solar cell. Our results indicates that the CZTSe solar cells made by using our newly designed stack layer and a (Zn,Sn)O buffer are promising for high-efficiency Cd-free CZTSe solar cells.