The magnetism, stabilities and phase transition of Ru in hcp, fcc, bct and bcc structures are investigated with detailed first-principles calculations based on density-functional theory and quasiharmonic lattice dynamics approximation. Magnetic ground states and stability ranges of various phases are obtained. Calculated results indicate that the non-magnetic (NM)-hcp structure is the most stable in the entire pressure range at zero temperature, and the structural transition cannot be induced by pressure alone. NM-fcc structure is a metastable phase of bulk Ru, while both the NM-bcc and ferromagnetic (FM)-bct structures are dynamically unstable. At high pressure and temperature, a transformation from NM-hcp to NM-fcc structure will occur. Finally, the pressure-temperature phase diagram of Ru is presented.