Large-scale simulations have been performed in the current-driven two-dimensional XY gauge glass model with resistively shunted junction dynamics, by means of a very effecient algorithm proposed before. It is found that the linear resistivity at low temperatures tends to zero, which indicates a finite temperature glass transition. Dynamical scaling analysis demonstrates that a nearly perfect collapse of current-voltage data can be achieved with the transition temperature T c =0.22 (in units of the Josephson coupling strength), dynamical critical exponent z=2.0, and the static exponent ν=1.2, which agrees quite well with recent findings by an equilibrium Monte Carlo simulations and finite-size scaling analysis in RSJ simulations.