Structural phase transitions and superconducting properties of platinum hydride under pressure are explored through the first-principles calculations based on the density functional theory. Three new low-pressure phases (Pm3m, Cmmm and P4/nmm) are predicted, and all of them are metallic and stable relative to decomposed cases. The superconducting critical temperature of two high-pressure phases correlates with the electron-phonon coupling. The presence of soft modes induced by Kohn anomalies and the hybridization between H and Pt atoms result in the strong electron-phonon coupling. Our results have major implications for other transition metal hydrides under pressure.