Three-dimensional (3D) printable hydrogels with a shape memory effect have emerged as a new class of 4D printing materials recently and found wide applications in various fields. However, synergistically endowing such materials with good mechanical strength and biocompatibility for biomedical uses remains challenging. In this study, a series of multiresponsive hydrogels have been prepared through a dynamic covalent imine/Diels-Alder network from biocompatible starting materials of modified gelatin and poly(ethylene glycol)-based polymers. By further secondary crosslinking with a hyperbranched triethoxysilane reagent (HPASi) that contains multiple supramolecular hydrogen bonding, the hydrogels presented a strengthened self-healing and temperature-responsive shape memory effect. With the additional features of superior stretchability (elongation at break up to 523%), good cytocompatibility, and 3D printable properties, these multifunctional hydrogels showed great potential for broad biomedical applications.