Bone tissue engineering (BTE) eliminates many problems associated with traditional treatments for repairing diseased or damaged bones. As an essential component of BTE, porous artificial scaffolds provide structural support and also a microenvironment for seeded live cells. These scaffolds should be made of osteoconductive biomaterials for promoting new bone formation. Additive manufacturing (AM, i.e., 3D printing) is a powerful platform for fabricating advanced tissue engineering scaffolds. It allows precise control of structural characteristics (pore shape and size, porosity, etc.) of scaffolds that significantly influence their properties (mechanical, transport, biological, etc.). Digital light processing (DLP), an AM technology, can provide micron-level printing resolution and high printed structure fidelity, making it attractive for developing new BTE scaffolds. Most of current research on DLP of BTE scaffolds uses pure bioceramic or biomedical polymers. In this study, a new osteoconductive nanocomposite, β-tricalcium phosphate (β-TCP)-reinforced poly(D,L-lactide-co-trimethylene carbonate) (PDLLA-co-TMC), was developed and its DLP 3D printing into BTE scaffolds was investigated. β-TCP is a biodegradable bioceramic with good osteoconductivity, while PDLLA-co-TMC is a shape-memory biodegradable polymer. The resulting shape-memory β-TCP/PDLLA-co-TMC scaffolds can be used in minimally invasive surgery for bone regeneration. Using acetone, β-TCP suspensions in PDLLA-co-TMC were made as printing inks for DLP. Inks with 0, 5, 10, 15, 20, 25, 30 vol% of β-TCP nanoparticles, respectively, together with PEGDA, curcumin-Na (free radical inhibitor), curcumin (photoabsorber) and LAP (photoinitiator), were prepared and DLP-printed into scaffolds of the designed grid structure with square pores. Photocuring was then conducted. These nanocomposite scaffolds showed high fidelity to the design, with a 400 micron pore size and strut size. The strength of nanocomposite scaffolds could reach 3.13 MPa, approaching that of human cancellous bone and hence indicating their suitability for BTE. Cytocompatibility assessment using MC3T3-E1 pre-osteoblasts through Live/Dead staining and CCK-8 assay showed good biocompatibility of DLP-printed nanocomposite scaffolds.