A simple band model using higher order non-parabolic effect was adopted for single layer molybdenum tungsten alloy disulfide (i.e., $\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$). The first-principles method considering $2\times2$ supercell was used to study band structure of single layer alloy $\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$ and a simple band (i.e., effective mass approximation model, EMA) model with higher order non-parabolic effect was used to fit the first-principle band structures in order to calculate corresponding the hole mobility. In addition, we investigate the alloy scattering effect on the hole mobility of $\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$.