Bioprinting is a new technology in regenerative medicine that allows the engineering of tissues by specific placement of cells in biomaterials. Importantly, the porosity and the relatively small dimensions of the fibers allow rapid diffusion of nutrients and metabolites. This technology requires the availability of hydrogels that ensure viability of encapsulated cells and have adequate mechanical properties for the preparation of structurally stable and well-defined three-dimensional constructs. The aim of this study is to evaluate the suitability of a biodegradable, photopolymerizable and thermosensitive A–B–A triblock copolymer hydrogel as a synthetic extracellular matrix for engineering tissues by means of three dimensional fiber deposition. The polymer is composed of poly(N-(2-hydroxypropyl)methacrylamide lactate) A-blocks, partly derivatized with methacrylate groups, and hydrophilic poly(ethylene glycol) B-blocks of a molecular weight of 10 kDa. Gels are obtained by thermal gelation and stabilized with additional chemical cross-links by photopolymerization of the methacrylate groups coupled to the polymer. A power law dependence of the storage plateau modulus of the studied hydrogels on polymer concentration is observed for both thermally and chemically cross-linked hydrogels. The hydrogels demonstrated mechanical characteristics similar to natural semi-flexible polymers, including collagen. Moreover, the hydrogel shows suitable mechanical properties for bioprinting, allowing subsequent layer-by-layer deposition of gel fibers to form stable constructs up to at least 0.6 cm (height) with different patterns and strand spacing. The resulting constructs have reproducible vertical porosity and the ability to maintain separate localization of encapsulated fluorescent microspheres. Moreover, the constructs show an elastic modulus of 119 kPa (25 wt% polymer content) and a degradation time of approximately 190 days. Furthermore, high viability is observed for encapsulated chondrocytes after 1 and 3 days of culture. In summary, we conclude that the evaluated hydrogel is an interesting candidate for bioprinting applications.