A novel ternary photocatalytic nanocomposite, Ag-Cu2O/C3N4, has been successfully synthesized via a facile two-step reduction procedure at room temperature, wherein Ag nanoparticles are directly growing on the surface of Cu2O supported by C3N4 nanosheets. The resulting ternary Ag-Cu2O/C3N4 photocatalyst exhibits enhanced photocatalytic activity towards methyl orange (MO) degradation compared with its counterparts (Cu2O, spherical Ag-Cu2O and Cu2O/C3N4), demonstrating a removal rate of MO up to 95.7% within 30 min. The enhanced photocatalytic activity can be ascribed to the following factors: (1) the surface plasmon resonance effect of Ag nanoparticles broadening the visible light response of Cu2O; (2) the introduction of C3N4 functioning not only as a fast electron delivery but also a fine stabilizer to prevent the Ag-Cu2O composite from agglomeration. Mechanism studies reveal that MO is cracked into smaller fragments and the h(+) is the main reactive species participating in the photocatalytic process. Moreover, the Ag-Cu2O/C3N4 photocatalyst also shows high photodegradation ability for another two representative azo dyes, acid orange II and congo red. This study demonstrates the potential of Ag-Cu2O/C3N4 in the degradation of azo dyes and also provides a guide to design of Cu2O-based ternary photocatalysts for further wastewater remediation.