In this study, we describe the preparation and characterization of a new class of thermoset hybrid networks containing aliphatic polyester and polyhedral oligomeric silsesquioxanes (POSS). The copper‐free 1,3‐dipolar cycloaddition click reaction of internal alkyne functionalized aliphatic polyester and multifunctional azido POSS with different concentrations led to highly crosslinked thermoset networks. The click reactions performed under ambient conditions (i.e., in tetrahydrofuran at room temperature for 1 day) in the absence of any catalyst. The chemical composition of hybrid networks and homogenous distribution of POSS molecules were confirmed by Fourier transform infrared spectroscopy and scanning electron microscopy with energy dispersive spectroscopy. The swelling ratios of hybrid networks were commonly decreased by increasing POSS‐N3 content and by changing polar solvents to apolar solvents. Thermogravimetric analysis results demonstrated that the thermal stability of hybrid networks increased with higher POSS feeding ratio. Tensile tests were applied to evaluate the mechanical properties of hybrid networks. Compared to neat aliphatic polyester, the mechanical properties of hybrid networks significantly improved. For instance, the tensile strength were enhanced from 5 MPa to 19 MPa by increasing the concentration of azido functionalized POSS from 10 to 40. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2222–2227