We have prepared single grain boundaries of the superconductor Ba1-xKxBiO3 by growing epitaxial thin films of this compound on SrTiO3 bicrystal substrates. The four-terminal current-voltage characteristics of the grain boundaries showed clear superconductor-insulator-superconductor (SIS) tunneling behavior. The leakage at zero bias was smaller than 0.3% at 4.2 K. The differential conductance displayed sharp symmetric peaks at 2 Delta close to 6.5 mV. At higher bias, an increase in conductance proportional to V-2 was observed. The temperature dependence of the conductance was found to be in qualitative accord with conventional SIS theory.