Two time series, taken simultaneously in the G-band and in white-light, and corrected for telescope aberrations and turbulence perturbations using the method of phase diversity, are employed to study the motions of granules and G-band bright points (GBPs) in the moat of an old regular sunspot. Local correlation tracking and feature tracking have been utilized for this purpose. A large-scale radial outflow with a mean velocity of 0.51 km s-1 has been measured in the sunspot moat. Centres of diverging horizontal motions, identified with families of granules formed by repeatedly splitting granules, move away from the sunspot. Most of the GBPs in the moat also move outwards through radially orientated ``channels'' (confined between the borders of adjacent families) with velocities comparable to those of the adjacent granules. However, 6% of the GBPs move faster (>1.4 km s-1) than the neighbouring granules. GBPs in the moat are not regularly distributed but they are less frequent on its solar centre side.