We demonstrate numerically that actively mode-locked semiconductor lasers employing a linearly-chirped fiber grating in an external cavity can exhibit multiple drive frequency ranges of stable pulse generation, and thus give a large locking bandwidth. The locking bandwidth defines the range of RF drive frequencies over which the laser will generate pulses with low timing jitter. The stable optical pulses are generated with leading or trailing subpulses due to optical energy circulating within the fiber grating. The multiple stable ranges merge if loss is introduced into the fiber-grating region. We also show that the locking bandwidth can be improved if chirp is introduced into the grating. Suprisingly, however, chirp of either sign improves the locking bandwidth.