Sodium alginate (SA)/chitosan (CH) polyelectrolyte scaffold is a suitable substrate for tissue-engineering application. The present study deals with further improvement in the tensile strength and biological properties of this type of scaffold to make it a potential template for bone-tissue regeneration. We experimented with adding 0%–15% (volume fraction) gelatin (GE), a protein-based biopolymer known to promote cell adhesion, proliferation, and differentiation. The resulting tri-polymer complex was used as bioink to fabricate SA/CH/GE matrices by three-dimensional (3D) printing. Morphological studies using scanning electron microscopy revealed the microfibrous porous architecture of all the structures, which had a pore size range of 383–419 µm. X-ray diffraction and Fourier-transform infrared spectroscopy analyses revealed the amorphous nature of the scaffold and the strong electrostatic interactions among the functional groups of the polymers, thereby forming polyelectrolyte complexes which were found to improve mechanical properties and structural stability. The scaffolds exhibited a desirable degradation rate, controlled swelling, and hydrophilic characteristics which are favorable for bone-tissue engineering. The tensile strength improved from (386±15) to (693±15) kPa due to the increased stiffness of SA/CH scaffolds upon addition of gelatin. The enhanced protein adsorption and in vitro bioactivity (forming an apatite layer) confirmed the ability of the SA/CH/GE scaffold to offer higher cellular adhesion and a bone-like environment to cells during the process of tissue regeneration. In vitro biological evaluation including the MTT assay, confocal microscopy analysis, and alizarin red S assay showed a significant increase in cell attachment, cell viability, and cell proliferation, which further improved biomineralization over the scaffold surface. In addition, SA/CH containing 15% gelatin designated as SA/CH/GE15 showed superior performance to the other fabricated 3D structures, demonstrating its potential for use in bone-tissue engineering.