Grain boundary Josephson junctions have been fabricated using high-quality epitaxial Hg-1212 HTS films grown on bicrystal SrTiO₃ substrates with a 24° misorientation angle. The films are prepared by the cation exchange method, with T_c between 120 K and 124 K. I-V characteristics of the junctions show typical RSJ behaviour. Critical current density obtained from junctions with different widths is uniform over a length scale of a few micrometres and is reproducible. The relatively high I_cR_n product at 77 K and 100 K and stability against thermal cycles show that the Hg-1212 junctions are promising for operations at temperatures higher than 77 K.