The invention relates to a furandicarboxylic acid copolyester and a preparation method thereof. The structural formula of the furandicarboxylic acid copolyester is shown in the following formula (1): wherein, x, y and z are all integers ranging from 10 to 90. Its preparation method includes the following steps: (1) mixing dibasic acid or its esterified product, dibasic alcohol and esterification reaction catalyst, and performing esterification reaction under an inert atmosphere to obtain the first intermediate product; wherein, the dibasic acid includes Furandicarboxylic acid, diols including ethylene glycol, 1,4-cyclohexanedimethanol and 2,2,4,4-tetramethyl-1,3-cyclobutanedimethanol; (2) under vacuum Under the condition of vacuum, the first intermediate product is subjected to precondensation reaction to obtain the second intermediate product; (3) under vacuum condition, the second intermediate product is subjected to polycondensation reaction to obtain furandicarboxylic acid copolyester. The preparation method of the present invention is simple, and the obtained furyl dicarboxylic acid copolyester has excellent heat resistance, transparency and mechanical properties at the same time, and can be used to manufacture baby feeding bottles, children's toys, water cups, kitchen supplies, electronic appliances and the like.