In this study, we investigate the Poisson's ratio of transition-metal dichalcogenides (TMDCs) with a chemical formula of MX2, where M = Mo, W and X = S, Se, respectively, from first-principles. Through density functional theory calculations, it is demonstrated that the Poisson's ratio of MX2 exhibits not only a substantial difference between the planar and vertical values but also a systematic dependence on the chalcogen species. Among the TMDCs, MoS2 displays the strongest anisotropy, which entails a distinctive contracting response under a planar strain. We find that such pronounced anisotropy in the Poisson's ratio of the TMDCs originates from the different filling of the in- (p(x), p(y), d(xy), and d(x2-y2)) and out-of-plane (pz, d(yz), d(zx), and d(z2)) electronic orbitals depending on the transition-metal elements. These findings shed a new light on the elastic properties of TMDCs which continue to be interesting and show intriguing phenomena.