The Cu₂ZnSnS₄ (CZTS) solar cell prepared on Si substrate has an advantage of low lattice mismatch between CZTS and Si substrate, but the conversion efficiency of reported p-CZTS/n-Si solar cells is still low at present. In this work, the CZTS solar cells on Si substrate are calculated numerically by heterojunction solar cell simulation software Afors-het. The calculated results show that the p-CZTS and n-Si act as window layer and absorber respectively in the p-CZTS/n-Si solar cell because the band gap of p-CZTS is larger than that of n-Si. The conversion efficiency of p-CZTS/n-Si solar cell increases as the thickness of p-CZTS window layer decreases. The highest calculated conversion efficiency of p-CZTS/n-Si solar cell is 18.57%. In the best p-CZTS/n-Si solar cell, most of the incident light cannot pass through the p-CZTS window layer due to the high absorption coefficient of p-CZTS, which limits the conversion efficiency of solar cell. In order to solve the problems existing in the p-CZTS/n-Si structure, a novel n-ZnO:Al/i-ZnO/n-CdS/p-CZTS/p-Si solar cell structure is proposed, where n-ZnO:Al and i-ZnO are window layers, n-CdS is buffer layer, p-CZTS is absorber, and p-Si is substrate and back electrode. The dark current density-voltage (J-V) characteristic curves of p-CZTS/p-Si structure varying with the thickness and doping concentration of p-Si and the doping concentration of p-CZTS are calculated to investigate the feasibility of p-Si as a back electrode of p-CZTS. All the calculated J-V characteristic curves of p-CZTS/p-Si structure are linear, indicating the formation of ohmic contact between p-CZTS and p-Si. The photovoltaic properties of n-ZnO:Al/i-ZnO/n-CdS/p-CZTS/p-Si solar cell are further calculated. The built-in electric field distributed in n-ZnO:Al, i-ZnO, n-CdS, and p-CZTS contribute to the collection of photo-generated carriers. The conversion efficiency of n-ZnO:Al/i-ZnO/n-CdS/p-CZTS/p-Si solar cell is enhanced with the decrease of the thickness of p-Si and the increase of doping concentrations of p-Si and p-CZTS and the thickness of p-CZTS. Without considering the effect of parasitic series resistance and parallel resistance and defect states, the highest conversion efficiency of ideal n-ZnO:Al/i-ZnO/n-CdS/p-CZTS/p-Si solar cell is 28.41%. The calculated results in this work show that the n-ZnO:Al/i-ZnO/n-CdS/p-CZTS/p-Si solar cell has an appropriate structure for CZTS solar cell on Si substrate.