Cavity growth on a sliding grain boundary to which a normal stress is applied is found to be faster than that on a stationary grain boundary. The morphology of the cavity contains an asymmetric crack-like tip which prompts surface diffusion locally when the sliding is dominant, and the growth rate becomes proportional to the third power of the normal stress independent of the sliding rate. Since the sliding rates of all grain boundaries are statistically comparable, only the normal stress dependence remains important. The conditions which favor the present mechanism are examined and shown to be in good agreement with the experimental evidence in creep cavitation.