The invention relates to a method for synthesizing high molecular weight polycarbonate, a catalyst and application in the technical field of polymer synthesis. The method comprises that diphenyl carbonate and dihydric alcohol as raw materials undergo a one-step melt transesterification polycondensation reaction to produce high molecular weight polycarbonate. The method can be widely used for aliphatic polycarbonate, aromatic polycarbonate, isosorbide-based polycarbonate and tricyclodecane dimethanol-based polycarbonate. After the transesterification polycondensation reaction, the catalyst canbe used as an inorganic filler directly residual in the polymer without separation and subsequent treatment. The catalyst is selected from a metal oxide and/or a metal-aluminum complex oxide and the metal is at least one of alkaline earth metals and zinc. Compared with the existing homogeneous catalyst systems such as a titanium group, a transition metal salt and a strong base, the catalyst used by the method has the advantages of simple preparation processes, low toxicity, good polymer color and no use of a catalyst in the separation process.