The aim of this research is to synthesize polycaprolactone-based polyurethanes (PCL-based PUs) that can be further used for the fabrication of guided bone regeneration (GBR) membranes with higher tensile strength and elongation at break than collagen and PTFE membranes. The PCL-based PUs were prepared by the polymerization of polycaprolactone (PCL) diol with 1,6-hexamethylene diisocyanate (HDI) at different ratios using either polyethylene glycol (PEG) or ethylenediamine (EDA) as chain extenders. The chemical, mechanical, and thermal properties of the synthesized polymers were determined using NMR, FTIR, GPC, DSC, and tensile tester. The PCL and polyurethanes were fabricated as nanofiber membranes by electrospinning, and their mechanical properties and SEM morphology were also investigated. In vitro tests, including WST-1 assay, SEM of cells, and phalloidin cytoskeleton staining, were also performed. It was shown that electrospun membranes made of PCL and PCL-HDI-PEG (2: 3: 1) possessed tensile strength of 19.84 MPa and 11.72 MPa and elongation at break of 627% and 362%, respectively. These numbers are equivalent or higher than most of the commercially available collagen and PTFE membrane. As a result, these membranes may have potential for future GBR applications.