It is highly desirable to reach a high carrier mobility in two-dimensional (2D) atomic crystals with a modest band gap for electronic applications. In this study, two 2D semiconducting materials, penta-PdX2 (X = P, As), are found to be promising candidates to approach this goal. Both penta-PdP2 and penta-PdAs2 have a band gap of about 0.7–0.8 eV. Their carrier mobility is up to 104 cm2 V−1 s−1 for electrons and 105 cm2 V−1 s−1 for holes, among the highest in 2D semiconductors. Moreover, the effective mass and band gap can be effectively tuned by applying a biaxial strain. The electron effective mass climbs up firstly and then largely declines under tensile load with a turning point at 5% for penta-PdP2 and 2% for penta-PdAs2. Furthermore, penta-PdX2 monolayers exhibit strong optical absorption in a wide wavelength range. All these outstanding properties render penta-PdX2 promising candidates for ultra-fast electronic and optoelectronic applications.