The invention relates to furan dicarboxylic acid copolyester and a preparation method thereof. The furan dicarboxylic acid copolyester has a structural formula as shown in a following formula (1), wherein x, y and z are integers of 10-90. The preparation method comprises the following steps: (1) mixing a dibasic acid or ester of the dibasic acid, dihydric alcohol and an esterification catalyst, and performing an esterification reaction in an inert atmosphere so as to obtain a first intermediate product, wherein the dibasic acid comprises furan dicarboxylic acid, and the dihydric alcohol includes ethylene glycol, 1,4-cyclohexane dimethanol and 2,2,4,4-tetramethyl-1,3-cyclobutane dimethanol; (2) performing a pre-polycondensation reaction on the first intermediate product under vacuum conditions so as to obtain a second intermediate product; and (3) performing a polycondensation reaction on the second intermediate product under vacuum condition so as to obtain the furan dicarboxylic acidcopolyester. The preparation method is simple, and the obtained furan dicarboxylic acid copolyester has excellent heat resistance, transparency and mechanical properties at the same time, and can be used for manufacturing baby nursing bottles, children toys, cups, kitchen utensils, electronic appliances and other products.