We have characterized highly conductive Si-doped GaN films with a high electron mobility of 112 cm2V−1s−1 at an electron concentration of 2.9 × 1020 cm−3, prepared using pulsed sputtering deposition (PSD). With an increase in the doping concentration, the absorption edge was found to shift toward a higher energy level, owing to the Burstein-Moss effect, thus making this material suitable for the transparent conductive tunneling electrodes of visible and ultraviolet-A light-emitting diodes. The full width at half maximum value of the near-band-edge (NBE) emissions in a photoluminescence spectrum measured at 77 K was as small as 185 meV, even for the sample with the highest electron concentration of 2.9 × 1020 cm−3. Such sharp NBE emissions from PSD-grown heavily Si-doped GaN films can be explained by an analytical model with a low compensation ratio θ of around 0.1, which is consistent with the exceptionally high observed electron mobility. These results indicate the strong potential of the low-temperature PSD growth technique for the formation of high-quality, heavily Si-doped GaN.