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By using the nonequilibrium Green’s function and the Landauer transport theory, nonlinear phonon properties in asymmetric graphene-based three terminal junctions (AGTTJs) are investigated. Results show that AGTTJs exhibit pronounced nonlinear thermal rectifying behaviors, and the efficiency is efficiently tuned by increasing the asymmetric degree between the left and right terminals or modulating the central probe. The thermal rectifying mechanism is analytically explained by the schematic diagram. It is suggested that AGTTJs may be served as a good ballistic thermal rectifier.