Two-dimensional (2D) transition-metal dichalcogenides (TMDs) exhibit intriguing properties for both fundamental research and potential application in fields ranging from electronic devices to catalysis. Based on first-principles calculations, we proposed a stable form of palladium diselenide (PdSe2) monolayer that can be synthesized by selenizing Pd(111) surface. It has a moderate band gap of about 1.10 eV, a small in-plane stiffness, and electron mobility larger than that of monolayer black phosphorus by more than one order. Additionally, tensile strain can modulate the band gap of PdSe2 monolayer and consequently enhance the infrared light adsorption ability. These interesting properties are quite promising for application in electronic and optoelectronic devices.