Three-dimensional (3D) bioprinting of photo-cross-linkable hydrogel precursors has attracted great interest in various tissue engineering and drug screening applications, as the biochemical and biophysical properties of the resultant hydrogel structures can be tuned spatiotemporally to provide cells with physiologically relevant microenvironments. In particular, these bioinks benefit from great biofunctional versatility that can be designed to direct cells toward a desired behavior. Despite significant progress in the field, the 3D printing of cell-laden photo-cross-linkable bioinks with low polymer concentrations has remained a challenge, as rapidly stabilizing these bioinks and transforming them to hydrogel filaments is hindered by their low viscosity. Additionally, reaching an optimized print condition has often been challenging due to the large number of print parameters involved in 3D bioprinting setups. Therefore, computational modeling has occasionally been employed to understand the impact of various print parameters and reduce the time and resources required to determine these effects in experimental settings. Here, we report a novel 3D bioprinting strategy for fabricating hydrogel fibrous structures of gelatin methacryloyl (GelMA) with superior control over polymer concentration, particularly in a relatively low range from ∼1% (w/v) to 6% (w/v), using a microfluidic printhead. The printhead features a coaxial core–sheath flow, coupled with a photo-cross-linking system, allowing for the in situ cross-linking of GelMA and the generation of hydrogel filaments. A computational model was developed to determine the optimal ranges of process parameters and inform about the diffusive and fluid dynamic behavior of the coaxial flow. The cytocompatibility of the biofabrication system was determined via bioprinting cell-laden bioinks containing U87-MG cells. Notably, the established pipeline from computational modeling to bioprinting has great potential to be applied to a wide range of photo-cross-linkable bioinks to generate living tissues with various material and cellular characteristics.