${Cu}_2\mathit{\text{ZnSn}}{S}_4(\mathit{\text{CZTS}})$ is a non-toxic earth abundant material and a promising quaternary semiconductor compound of groups $I-II-IV-VI$ having a kesterite symmetrical structure. Due to its optimum direct bandgap, it has been considered as a suitable material for absorber layers for photovoltaic cell applications. This paper presents the numerical simulation and modeling of $\mathit{\text{CZTS}}$ based thin film kesterite photovoltaic cells using SCAP-1D software. The influence of device parameters such as the carrier concentration, thickness, densities of absorber, buffer and window layers, defect densities and the temperature effect on the performance of the $ZnO/CdS/\mathit{\text{CZTS}}/Mo$ photovoltaic cell structure are analyzed. Defect densities are added to the absorber layer and the interface between the buffer layer and the absorber layer. This type of solar cell does not comprise any toxic material and can lead to non-toxic thin film photovoltaic cells with outstanding optical properties. In this work, promising optimized results had been achieved with a conversion efficiency of 23.72%, a fill factor of 82.54%, a short-circuit current ($J_{sc})$ of 44.87 ${\text{mA}/\text{cm}}^2$ , and an open circuit voltage ${(V}_{oc})$ of 0.64V.