The use of porous three-dimensional (3D) composite scaffolds has attracted great attention in bone tissue engineering applications because they closely simulate the major features of the natural extracellular matrix (ECM) of bone. This study aimed to prepare biomimetic composite scaffolds via a simple 3D printing of gelatin/hyaluronic acid (HA)/hydroxyapatite (HAp) and subsequent biomineralization for improved bone tissue regeneration. The resulting scaffolds exhibited uniform structure and homogeneous pore distribution. In addition, the microstructures of the composite scaffolds showed an ECM-mimetic structure with a wrinkled internal surface and a porous hierarchical architecture. The results of bioactivity assays proved that the morphological characteristics and biomineralization of the composite scaffolds influenced cell proliferation and osteogenic differentiation. In particular, the biomineralized gelatin/HA/HAp composite scaffolds with double-layer staggered orthogonal (GEHA20-ZZS) and double-layer alternative structure (GEHA20-45S) showed higher bioactivity than other scaffolds. According to these results, biomineralization has a great influence on the biological activity of cells. Hence, the biomineralized composite scaffolds can be used as new bone scaffolds in bone regeneration.