Three-dimensional (3D) bioprinting is a technology that can precisely fabricate customized tissues and organs. Hydrogel materials that can embed living cells for use in 3D printing are called bioinks. However, there are only limited options of bioinks currently because they require the following features at once, such as printability, repetitive layer-by-layer stacking (stackability), structure stabilization, and biological properties. A polyurethane-gelatin double network hydrogel bioink was previously reported to own tunable modulus through changing the solid content, but cell viability at the high solid content is inevitably reduced. In the present study, the reinforcement effects of a metal-organic framework (MOF), zeolitic imidazolate framework-8 (ZIF-8), in the PUG bioink were evaluated. The printability, stackability, thermoresponsiveness, and shear-thinning behavior of the PUG-ZIF-8 composite hydrogels were examined. It was found that the PUG composite hydrogel containing 1250 μg/mL ZIF-8 crystals showed significant structural stability and modulus enhancement (∼2.5-fold). However, the PUG bioink containing 1250 μg/mL ZIF-8 crystals may lead to cell senescence or death. The cytocompatible concentration of ZIF-8 crystals in the bioink was about 875 μg/mL, and this concentration was much higher than the reported tolerable amount (∼50 μg/mL) of ZIF-8 for biomedical applications. The strong reinforcement effect of ZIF-8 and the drug-loading/sensing possibilities of MOFs may open new opportunities for using MOFs in 3D bioprinting applications.