Recently, studies by Jure Grgic et al. (Phys. Rev. Lett. 108 183903, 2012) show that in a periodic structure, the large gain can be eventually turned to decreasing the effect of slow light on the structure. In this paper, one-dimensional periodic structures are taken as an instance, and the influences of gain on slow light are further investigated. It is shown that different influences can exhibit in the finite-length and infinite-length one-dimensional periodic structures. For the infinite-length structures, the addition of gain can decrease the slow light effect, whereas for finite-lengh structures, the compensation of gain can, to a certain degree, increase the slow light effect. Our results verify a feasible way in the application of such a periodic structure, as a slow-light device, and especially as the tunable slow-light devices, in the high-density integration of optical circuits.