Scaffolds with controlled drug release are valuable for bone tissue engineering, but constructing the scaffolds with controllable dual-drug release behaviors is still a challenge. In this study, layered mesoporous bioactive glass/sodium alginate-sodium alginate (MBG/SA–SA) scaffolds with controllable dual-drug release behaviors were fabricated by 3D printing. The porosity and compressive strength of three-dimensional (3D) printed MBG/SA–SA scaffolds by cross-linking are about 78% and 4.2 MPa, respectively. As two model drugs, bovine serum albumin (BSA) and ibuprofen (IBU) were separately loaded in SA layer and MBG/SA layer, resulting in a relatively fast release of BSA and a sustained release of IBU. Furthermore, layered MBG/SA–SA scaffolds were able to stimulate human bone mesenchymal stem cells (hBMSCs) adhesion, proliferation and osteogenic differentiation than SA scaffolds. Hence, the 3D printed MBG/SA–SA scaffolds would be prospective for the treatment of bone defects.