The invention provides a ternary supported catalyst and a preparation method and application thereof.The ternary supported catalyst comprises a carrier and an auxiliary loaded on the surface of the carrier, the carrier comprises In2O3 and an M-containing
oxide, the M-containing
oxide comprises ZrO2, Ga2O3 or ZnO, and the auxiliary comprises an
Rh element, a
Pd element and a
Cu element; in the ternary supported catalyst, the content of an
Rh element is 1 to 10 weight percent, the content of a
Pd element is 0.1 to 5 weight percent, and the content of a
Cu element is 0.8 to 10 weight percent. According to the ternary supported catalyst disclosed by the invention, three elements of Rh, Pd and Cu with specific contents are supported on a specific carrier, and the contents of the Rh, Pd and Cu elements in the catalyst are regulated, so that the ternary supported catalyst has the characteristics of high CO2 conversion rate, high
methanol selectivity, high
methanol space-time yield and the like.