By using small-amplitude approximation on continuous wave bsckground, the gain dispersion and two-photon absorption supported small-amplitude dark optical soliton solutions are analytically studied in this paper. Their features of evolution in the various regions in parameter space are discussed. The result shows that the small-amplitude dark solitons are stable in some regions, but are constable in other regions in which the smallamplitude saute of the dark soliton will contains until excessed certain propagating distance.