Chevrel-phase superconducting compounds A(y)Mo(6)Q(8) (A = Pb, Mg, etc. and Q = S, Se, Te) have attracted much attention due to their ultrahigh upper critical magnetic fields (H-c2). However, the binary compounds Mo6S8 and Mo6Te8 show no superconducting properties above 2 K. In this work, the new Chevrel-phase pseudobinary compound Mo6S6.8Te1.2 with a superconducting transition temperature (T-c) of 3.6 K was successfully synthesized by a two-step process. A detailed investigation implies that the superconductivity in Mo6S6.8Te1.2 may derive from the increased electronic density near the Fermi level in comparison to Mo6S8. Our work provides a feasible scheme to search for new superconducting compounds.