In this work, ${\beta}$-gallium oxide thin film was investigated for enhancing the optical and electrical properties deposited through physical vapour deposition powered by radio frequency sputtering method at optimized parameters of deposition rate and surface roughness based on Taguchi–grey relational approach. Taguchi L8 (2$^4$) orthogonal array DOE were selected based on 2 levels of plasma power (P), working pressure ($P_r$), standoff distance between target and substrate (D), and deposition time (T). From the analysis of Taguchi–grey relational approach, the optimal parameters were predicted as ‘P1-D2-Pr2-T2’, which showed good improvement on GRG of 0.0165 over initial parameter settings. Predicted parameters were further validated by depositing thin films for deposition rate and surface roughness by varying plasma power of optimal parameter. On analysis, deposition rate and surface roughness showed better results in case of 75 W, as compared to other plasma power (100 and 50 W). Therefore, ${\beta}$-Ga$_2$O$_3$ thin films deposited at optimal parameter were further investigated for optical and electrical properties. Field-emission scanning electron microscopy results suggested that thin films grown were uniform, dense and defects free. Thin films showed nanocrystalline structure with small peak at 2${\theta}$ = 38°, oriented in the (–311) plane. The maximum transmittance was obtained as ${\sim}$63% in the visible 300–900 nm wavelength, while the band energy gap calculated from the Tauc plot obtained was 3.79 eV. The electrical resistivity of the thin films was 1.067 ${\times}$ 10$^4$ ${\Omega}$ cm. Thus, all results suggest that thin films grown at optimized parameters enhance the optical and electrical properties and also showed potential to further use for optoelectronics device at short wavelengths.