Poly(ε-caprolactone)-based non-woven fibrous mats showing excellent one-way shape memory properties were obtained through a straightforward approach by combining electrospinning process and sol–gel reaction. A solution of partially crosslinked α,ω-triethoxysilane-terminated poly(ε-caprolactone) was used to obtain bead-free fibers through electrospinning. Non-woven mats with different crosslinking degrees have been prepared and the effect of the different crosslinking extent and of the microfibrous structure were correlated to the mechanical and shape memory properties of the material. The evolution of fiber architecture within the non-woven mat following deformation and shape memory cycles was also investigated.