The field of tissue engineering is rapidly adopting the principles of additive manufacturing, which provides a means to generate complex functional tissue constructs in a programmable manner with micron-scale precision. Most hydrogel-based 3D bioprinting results in mechanically soft and weak constructs, which are not suitable for practical tissue engineering applications. Increasing the stiffness of the hydrogel in general results in entrapment of the encapsulated cells, leading to suboptimal biological responses. Here, we report a bioprinting process that provides dynamic control over stiffness and strength of the printed hydrogel-cell constructs with optimal cell spreading. The bioink consists of gelatin, gelatin methacryloyl (GelMA) and alginate, with each component crosslinked by enzymatic, photopolymerization and ionic crosslinking, respectively, to form interpenetrating networks (IPNs). The formation of IPNs significantly improved mechanical properties and stability of the printed structures. Temporal control of each crosslinking mechanism resulted in excellent cell spreading, avoiding the usual cell entrapment in the stiff 3D hydrogel environment, while achieving much improved mechanical properties of the constructs. This novel bioprinting process is expected to become a useful tool for producing mechanically robust tissue-like structures.