Since the traditional 2D surface for cell growth has been shown to be increasingly insufficient in contemporary cell biology, more and more research is performed on 3D matrices that can better represent the natural extracellular matrix (ECM) in many aspects. To create such a complex nonuniform 3D matrix, four‐armed polyethylene glycol with azides and (1R,8S,9S)‐bicyclo[6.1.0]non‐4‐yn‐9‐yl groups is functionalized to form the hydrogel basis. Together with these, a matrix metalloproteinase cleavable peptide sequence as a functional motif is also built in to add degradability to the hydrogel. In addition, self‐assembled peptide amphiphile (PA) fibers containing a cellular binding peptide sequence (RGDS) are encapsulated in the hydrogel to mimic the natural fibrous structure of the ECM and to stimulate cell adhesion. Rheology studies confirm that the polymer dissolved in the PA fiber solution forms a stable hydrogel with acceptable mechanical properties (G′ = 3.8 kPa). In addition, it is shown that this hydrogel network is degradable under the action of a metalloproteinase enzyme. Finally, the hybrid hydrogel is used to culture and it is demonstrated that both HeLa cells and human mesenchymal stem cells show adherence, good viability, and a well‐spread shape inside the hybrid hydrogel after 5 days of incubation when all components are present.