La-doped SrSnO3 (LSSO) is known as one of deep-ultraviolet (DUV)-transparent conducting oxides with an energy bandgap of ~4.6 eV. Since LSSO can be grown heteroepitaxially on more wide bandgap substrates such as MgO (Eg ~7.8 eV), LSSO is considered to be a good candidate as a DUV-transparent electrode. However, the electrical conductivity of LSSO films are below 1000 S cm^-1, most likely due to the low solubility of La ion in the LSSO lattice. Here we report that high electrically conducting (>3000 S cm^-1) LSSO thin films with an energy bandgap of ~4.6 eV can be fabricated by pulsed laser deposition on MgO substrate followed by a simple annealing in vacuum. From the X-ray diffraction and the scanning transmission electron microscopy analyses, we found that lateral grain growth occurred during the annealing, which improved the activation rate of La ion, leading to a significant improvement of carrier concentration (3.26 x 10^20 cm^-3) and Hall mobility (55.8 cm^2 V^-1 s^-1). The present DUV-transparent oxide semiconductor would be useful as a transparent electrode for developing optoelectronic devices, which transmit and/or emit DUV-light.