While pyrite-type PtBi_{2} with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a PtBi_{2} single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to (11.2×10^{6})% at T=1.8 K in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as WTe_{2}, LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov-de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite PtBi_{2} is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.