The invention discloses furan dicarboxylic acid copolyester and a preparation method thereof. Monomers for preparing the furan dicarboxylic acid copolyester comprise: a component (a) of furan dicarboxylic acid or furan dicarboxylate, a mixture component (b) of cis-1,4-cyclohexyldimethanol and trans-1,4-cyclohexyldimethanol and a component (c) which is one or an arbitrary proportional mixture of more of ethylene glycol, propylene glycol and butanediol, wherein the trans-1,4-cyclohexyldimethanol in the component (b) accounts for 0.1-60.0 mol% or 70.0-99.9 mol% in the total amount of the cis-1,4-cyclohexyldimethanol and trans-1,4-cyclohexyldimethanol. The prepared furan dicarboxylic acid copolyester has the advantages of high molecular weight, high crystallization speed, high modulus and strength, good barrier performance for oxygen and carbon dioxide and light color, and can meet application requirements in packaging materials, film, fiber, engineering plastic and other fields.