Three-dimensional (3D) bioprinting is a technology under active study for use in tissue engineering and regenerative medicine. Bioink comprises cells and polymers and is the essential material for 3D bioprinting. The characteristics of the bioink affect its printability, gelation behavior, and cell compatibility. In this study, alginate derivatives were synthesized to induce rapid gelation, and a bioink was prepared by mixing these alginate derivatives with silk fibroin to enhance cell compatibility. A low-concentration (3 wt %) alginate/silk fibroin (Alg/SF) bioink was pregelated by the ionic cross-linking of Alg to increase the viscosity for 3D printing. The rheological and mechanical properties were analyzed using a rheometer and a texture meter, respectively. Analysis of cell viability and proliferation using fibroblasts (NIH-3T3) in the bioinks showed that the Alg/SF bioink has improved cytocompatibility compared to that of conventional Alg bioinks, making it a promising material for tissue engineering.