Biomineralization is the process by which biominerals, minerals composed of bioinorganic matter possessing a controlled structure and orientation and a biomacromolecular assembly with an ordered structure that acts as a 3D template, are formed. In this study, we investigated the fabrication of organic/inorganic hybrid gels by bioinspired mineralization in peptide hydrogels. An Ac-(VHVEVS)3-CONH2 peptide was used as a multifunctional template with a mineral source supply capability and structural controllability that facilitates the formation of hydrogels via self-assembly. Hydrogels with varying viscoelastic strengths were prepared from the designed peptide by controlling the concentration of calcium ions added as cross-linking agents. The peptide hydrogel supplied carbonate anions as the mineral source through the hydrolysis of urea and mineralized CaCO3 with controlled morphology on the peptide network. With increases in the concentration of calcium ions added, the morphology of the mineralized CaCO3 changed from a fibrous structure to a thin film. This implies that the nucleation and growth mechanisms of CaCO3 formed by bioinspired mineralization were affected not only by the morphology and supply rate of the mineral source by the peptide network acting as a multifunctional template, but also by the viscoelastic strength of the hydrogel that served as a 3D reaction field.