The excess Fe atoms which unavoidably exist in the Fe(Te, Se, S) crystal lattice result in a complicated antiferromagnetic ground state as well as the suppression of superconductivity. As a result, there are still discrepancies on their phase diagrams. In this paper, we report the synthesis of Fe1+δTe1-xSx (0 ≤ x ≤ 0.12) single crystals by a melting method. Superconductivity was greatly improved after air annealing by which we partially removed the excess Fe atoms. Based on the resistivity and susceptibility measurements, we concluded a phase diagram of the Fe1+δTe1-xSx (0 ≤ x ≤ 0.12) system with fewer excess iron atoms. We found a coexisting region (0.07 ≤ x ≤ 0.11) of antiferromagnetic order and bulk superconductivity. This phase diagram is similar to that of the K- or Co-doped BaFe2As2 system, as well as the Fe(Te, Se) system, implying a commonality of the iron-based superconductors.