The invention discloses a ternary catalyst for preparing fatty group polycarbonate, comprising three components of boron hydrogenation rare earth, zinc alkyls and glycerol, wherein the structure of the boron hydrogenation rare earth is M(BH4)3, and M is one of rare earth elements of Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb and Lu; the zinc alkyls is diethyl zinc, zinc n-propyl, zinc isopropyl, zinc normal-butyl, zinc isobutyl or zinc benzyl. The ternary catalyst has easy acquirement of raw materials, simple preparation method and low cost, the fatty group polycarbonate with the number-average molecular weight exceeding 16000 and the weight-average molecular weight exceeding 45000 can be prepared, and the carbon dioxide fixation rate exceeds 36%.