Tin-chalcogenides SnX (X=Te, Se, and S) have been attracting research interest due to their thermoelectric physical properties. Their two-dimensional (2D) counterparts, which are expected to enhance those properties, nevertheless have not been fully explored because of many possible structures. A variable-composition exploration of 2D Sn1-xXx systems (X=Te, Se, and S) has been performed using a global searching method based on an evolutionary algorithm combined with density-functional calculations. A new hexagonal phase denoted by β′-SnX is found using Universal Structure Predictor: Evolutionary Xtallography (USPEX), and the structural stability has been further checked by calculations of phonons and elasticity. β′-SnTe is the most stable among all possible 2D phases of SnTe, including experimentally available phases. Further, β′ phases of SnSe and SnS are also found to be energetically close to the most stable phases. A high thermoelectronic (TE) performance has been predicted in the β′-SnX phases, which have a dimensionless figure of merit as high as ∼0.96 to 3.81 for SnTe, ∼0.93 to 2.51 for SnSe, and ∼1.19 to 3.18 for SnS at temperatures ranging from 300 to 900 K with a practically attainable carrier concentration of 5×1012cm-2. The high TE performance results from a high power factor that is attributed to the quantum confinement of 2D materials and the band convergence near the Fermi level, as well as low thermal conductivity mainly from both low elastic constants due to weak inter-Sn bonding strength and strong lattice anharmonicity.