In this paper,We investigate physical properties of Gd doped stable wurtzite (w-GaN) using Wien2K code, by employing DFT+U. We consider pure GaN and we dope Gd concentration 6.25% into the host GaN lattice. We elaborate and present a detailed electronic, optical and thermoelectric properties of Gd0.06Ga0.94N. The absorption coefficient has been enhancing in the ultraviolet (UV) region. That system is mostly suitable for UV optoelectronics. Our results, on the optical properties suggest this material for potential uses in UV optoelectronics, LEDs, and photovoltaics. The thermoelectric properties as a temperature were studied by solving the BoltzTrap transport equations in conjunction with Density Functional Theory (DFT). In this work, we present the theoretical results of electric conductivity, Seebeck coefficient, power factor and figure-of-merit. Our predictions for temperature dependence of electrical conductivity and power factor revealed a promising use of Gd0.06Ga0.94N for high temperature thermoelectric applications. It was found that the thermoelectric figure-of-merit for at T=250 K is about 0.37 while it can reach 1.29 at 800 K on n-type and about 2.51 at 800 K on p-type.