2,5-Bis(hydroxymethyl)furan is a highly valuable biobased rigid diol resembling aromatic monomers in polyester synthesis. In this work, it was enzymatically polymerized with various diacid ethyl esters by Candida antarctica Lipase B (CALB) via a three-stage method. A series of novel biobased furan polyesters with number-average molecular weights (M-n) around 2000 g/mol were successfully obtained. The chemical structures and physical properties of 2,5-bis(hydroxymethyl)furan-based polyesters were fully characterized. Furthermore, we discussed the effects of the number of the methylene units in the dicarboxylic segments on the physical properties of the furan polyesters.