Glycine (Gly), which is the simplest amino acid, induces the inflammation response and enhances bone mass density, and particularly its β polymorph has superior mechanical and piezoelectric properties. Therefore, electrospinning of Gly with any polymer, including polyvinyl alcohol (PVA), has a great potential in biomedical applications, such as guided bone regeneration (GBR) application. However, their application is limited due to a fast degradation rate and undesirable mechanical and physical properties. Therefore, encapsulation of Gly and PVA fiber within a poly(ε-caprolactone) (PCL) shell provides a slower degradation rate and improves the mechanical, chemical, and physical properties. A membrane intended for GBR application is a barrier membrane used to guide alveolar bone regeneration by preventing fast-proliferating cells from growing into the bone defect site. In the present work, a core/shell nanofibrous membrane, composed of PCL as shell and PVA:Gly as core, was developed utilizing the coaxial electrospinning technique and characterized morphologically, mechanically, physically, chemically, and thermally. Moreover, the characterization results of the core/shell membrane were compared to monolithic electrospun PCL, PVA, and PVA:Gly fibrous membranes. The results showed that the core-shell membrane appears to be a good candidate for GBR application with a nano-scale fiber of 412 ± 82 nm and microscale pore size of 6.803 ± 0.035 μm. Moreover, the wettability of 47.4 ± 2.2° contact angle (C.A) and mechanical properties of 135 ± 3.05 MPa average modulus of elasticity, 4.57 ± 0.04 MPa average ultimate tensile stress (UTS), and 39.43% ± 0.58% average elongation at break are desirable and suitable for GBR application. Furthermore, the X-ray diffraction (XRD) and transmission electron microscopy (TEM) results exhibited the formation of β-Gly.