Angiogenesis–osteogenesis coupling processes are vital in bone tissue engineering. Normal biomaterials implanted in bone defects have issues in the sufficient formation of blood vessels, especially in the central part. Single delivery of vascular endothelial growth factors (VEGF) to foci in previous studies did not show satisfactory results due to low loading doses, a short protein half-life and low efficiency. Development of a hypoxia-mimicking microenvironment for cells by local prolyl-4-hydroxylase inhibitor release, which can stabilize hypoxia-inducible factor 1α (HIF-1α) expression, is an alternative method. The aim of this study was to design a dimethyloxallyl glycine (DMOG) delivering scaffold composed of mesoporous bioactive glasses and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) polymers (MPHS scaffolds), so as to investigate whether the sustained release of DMOG promotes local angiogenesis and bone healing. The morphology and microstructure of composite scaffolds were characterized. The DMOG release patterns from scaffolds loaded with different DMOG dosages were evaluated, and the effects of DMOG delivery on human bone marrow stromal cell (hBMSC) adhesion, viability, proliferation, osteogenic differentiation and angiogenic-relative gene expressions with scaffolds were also investigated. In vivo studies were carried out to observe vascular formations and new bone ingrowth with DMOG-loaded scaffolds. The results showed that DMOG could be released in a sustained manner over 4 weeks from MPHS scaffolds and obviously enhance the angiogenesis and osteogenesis in the defects. Microfil perfusion showed a significantly increased formation of vessels in the defects with DMOG delivery. Furthermore, micro-CT imaging and fluorescence labeling indicated larger areas of bone formation for DMOG-loaded scaffolds. It is concluded that MPHS–DMOG scaffolds are promising for enhancing bone healing of osseous defects.