Kinetics of diffusion-limitied aggregation-annihilation processes on NW small-world networks is investigated by Monte Carlo simulation. In the system, if two clusters of the same species meet at the same node, they will aggregate and form a large one; while if two clusters of different species meet at the same node, they will annihilate each other. Simulation results show that, if the value of p (a parameter that quantifies the number of shortcuts) is large or small enough, the concentration of clusters c(t) and the concentration of particles g(t) follow power laws at large times, i.e.c(t)∝t-α and g(t)∝t－β. Moreover, the relation between the exponents α and β is found to satisfy α=2β. However, if p is of medium value, the concentration of clusters and the concentration of particles do not follow the power laws exactly. Our simulation results agree with the reported theoretical analysis very well.