Simple sandpile models show the self-organized criticality(SOC). Small-world networks serve as the hybrids of lattice graphs and random graphs. By numerical simulations of the sandpiles on small-world networks we find that when the randomness of the network is larger than 0.03~0.1, the exponents of the distributions of avalanche sizes and durations are increased and the one relating avalanche size to its duration is decreased. This result is explained by means of the concepts of characteristic path lengths and clustering coefficients of the small-world networks.
