Synthesis of high molecular weight alternating copolymers from epoxides and norbornene anhydride via metal-free catalyst remains a challenge in aliphatic biodegradable polyester synthesis. Metal-free Lewis pair catalyst system, consisting of Lewis acid B(C 2 H 5 ) 3 (triethylborane) and a Lewis base DMAP (4-dimethylaminopyridine); TBD (1, 5, 7-triazabicyclo[4.4.0]dec-5-ene) and DBU (1,8 diazabicyclo[5.4.0]undec-7-ene) as a cooperative catalyst system for fully alternating polyesters synthesis is described here. By using these simple systems we have obtained, high molecular weight (M n = 2–31.5 kDa) polyesters with narrow molecular weight distributions (MWD's = 1.948–1.069) via ring-opening alternating copolymerisation (ROAC) of various epoxides (e.g. CHO, cyclohexene oxide; PO, propylene oxide; tBGE, tert-butyl glycidyl ether and PGE, phenyl glycidyl ether) with cis-5 norbornene-endo 2, 3 dicarboxylic anhydride (NB). Furthermore, we demonstrated that these polyesters are biocompatible in nature when tested on human embryonic kidney cells (HEK-293) showing more than 80% cell viability in 72 h and can be used for different biological applications such as drug delivery, tissue engineering or anti-microbial polymeric coatings on biomedical devices. The use of these green functional polyesters for biological studies was realized for the first time by a metal-free Lewis pair approach. © 2019 Elsevier Ltd