The cascade failures in scale-free networks with community structure are studied and cascade propagation of such networks with different modularity parameters is simulated. It is found that the network with small modularity is much easier to trigger cascade failures than that of the larger one. Furthermore, different removal strategies have some what large effects on the cascade failures aftereffect. The simulations also show that larger modularity and reserve capacity coefficient will delay the breakdown caused by a cascade of network. This is particularly important for such real networks with community as traffic networks, distribution networks, and electrical power grids.