We carried out first-principles calculations to investigate the electronic properties of the monolayer blue phosphorene (BlueP) decorated by the group-IVB transition-metal adatoms (Cr, Mo and W), and found that the Cr-decorated BlueP is a magnetic half metal, while the Mo- andW-decorated BlueP are semiconductors with band gaps smaller than 0.2 eV. Compressive biaxial strains make the band gaps close and reopen and band inversions occur during this process, which induces topological transitions in the Mo-decorated BlueP (with strain of ??5:75%) and W-decorated BlueP (with strain of ??4:25%) from normal insulators to topological insulators (TIs). The TI gap is 94 meV for the Mo-decorated BlueP and 218 meV for the W-decorated BlueP. Such large TI gaps demonstrate the possibility to engineer topological phases in the monolayer BlueP with transition-metal adatoms at high temperature.