Recent studies on three-dimensional (3D) bioprinting of cell-laden gelatin methacryloyl (GelMA) hydrogels have provided promising outcomes for tissue engineering applications. However, the reliance on the use of photo-induced gelation processes for the bioprinting of GelMA and the lack of an alternative crosslinking process remain major challenges for the fabrication of cell-laden structures. Here, we present a novel crosslinking approach to form cell-laden GelMA hydrogel constructs through 3D embedded bioprinting without using any external irradiation that could drastically affect cell viability and functionality. This approach consists of a one-step type of crosslinking via bisulfite-initiated radical polymerization, which is combined with embedded bioprinting technology to improve the structural complexity of printed structures. By this means, complex-shaped hydrogel bio-structures with cell viability higher than 90% were successfully printed within a support bath including sodium bisulfite. This study offers an important alternative to other photo-induced gelation processes to improve the bio-fabrication of GelMA hydrogel with high cell viability.