Three-dimensional (3D) bioprinting is a powerful technique for the production of tissue-like structures to study cell behavior and tissue properties. A major challenge in 3D extrusion bioprinting is the limited diversity of bioinks, which fulfills the requirements of shear-thinning and strain recovery behaviors and can be solidified by a crosslinking process to retain their shape after printing. Herein, we aimed to develop a natural biopolymer-based formula with dual crosslinking performance to formulate a cell-laden bioink. In this study, methacrylate gelatin (GelMA) and methacrylated silk fibroin (SFMA) with different degrees of methacrylation were fabricated into hybrid bioinks. The GelMA/SFMA bioink of an optimal degree provides excellent rheological properties for extrusion bioprinting, and its hydrogel precursor polymer can form a polymer network at a low temperature and the high shape fidelity of the printed construct through photocrosslinking. Moreover, the hydrogel bioink can encapsulate different types of cells together to create 3D printed constructs that mimic the cellular microenvironment at a microscale level. Human umbilical vein endothelial cells (HUVECs) and rat pheochromocytoma (PC12) cells encapsulated in the 3D printed constructs can maintain high viability and proliferation ability for a long time. Furthermore, the GelMA/SFMA hydrogels were implanted in the subcutaneous tissue of SD rats for the evaluation of biocompatibility and degradability in vivo. Thus, the proposed GelMA/SFMA bioink expands the palette of available bioinks and offers opportunities for biomedical applications such as tissue engineering and soft robotics in clinical applications.