Inorganic–organic hybrid materials have promising properties for bone repair because of their covalent bonding between the inorganic and organic phases. This fine interaction allows us to overcome the limitations of composite materials, such as inhomogeneous biodegradation rates and non-biointeractive surfaces. In this study, a polycaprolactone (PCL)-based polyurethane (PU) with an organosilane functional group was synthesized for the first time. Thereafter, a biodegradable PU-silica hybrid was produced through a sol-gel process. The PU-silica hybrid was not only tough and flexible but also fully biodegradable. In addition to this, the urethane bonding enabled the silane coupling agent to increase crosslinking between the polymer and silica network, as well as between polymer to polymer. Accordingly, a rapid sol-to-gel gelation time was required to produce the hybrids, which allowed the production of 3D porous hybrid scaffolds through a simple salt-leaching process. A hybrid scaffold with 30 wt. % silica composition was the most ideal material for a bone regenerative scaffold since it was able to withstand thermal deformation with promising mechanical properties. Moreover, the hybrid scaffold induced osteogenic differentiation and angiogenesis, to accelerate bone regeneration.