A series of novel biobased polyesters are synthes i z e d b y i n t r o d u c i n g d i f u r a n y l m o n o m e r s -b i s -(hydroxymethylfurfuryl)amines (BHMFAs) and 2,5-furandicarboxylate (FDCA) for the first time under mild condensation conditions, in which both FDCA and BHMFAs are derived from the biomass platform chemical 5-hydroxymethylfurfural. The special structure of the polyesters, in which the structural repeating unit contains three furan rings and alterable side chains (ethyl, heptyl, dodecyl, benzyl, and phenethyl groups), endows their controllable performance, conformation, and free volume. The results showed that all of the polyesters are amorphous, confirmed by the results of DSC, XRD, and density functional theory. Different side chains of the polyesters result in T g s varying from 3.5 to 51.6 °C, tensile moduli from 3 to 551 MPa, and elongations at break from 13 to 1100%. Significantly, the polyester with phenethyl as the side chain shields ∼100% UV light. The polyester with benzyl as the side chain reduces gas permeability coefficients (PCO 2 and PO 2 ) by approximately three times compared with poly (ethylene terephthalate) (PET), which can be well explained by fractional free volume calculation results from molecular dynamics simulation. In addition, the polyesters show high dielectric constants (ε = 4.01−4.58) and maintain relatively low dielectric loss (tanδ = 0.023−0.043). This work provides strategies for designing and synthesizing biopolyesters with rigid to flexible structures, excellent UV shielding, gas barriers, and dielectric properties by varying the structure of the side chains and by introducing the difuran ring group.