Here, we have identified the monolayer phase of Bi2O2Se as a promising two-dimensional semiconductor with ultra-high carrier mobility and giant electric polarization. Due to the strong reconstruction originated from the interlayer electrostatic force, we have applied structure prediction algorithms to explore the crystalline geometry of Bi2O2Se monolayer with the lowest total energy. Considering Se and Te belong to the same group, Bi2O2Te monolayer is also investigated based on a similar scheme. Further calculations suggest that the high carrier mobility is maintained in the monolayer phase and the moderate band gap will lead to the strong optical absorption in the visible light region. In particular, the electron mobility in Bi2O2Te can reach as high as 3610 cm2V-1s-1 at room temperature, which is almost ten times of conventional transition metal dichalcogenides (TMD) family. Because of the strong structural anisotropy, a remarkable spontaneous in-plane and out-of-plane electric polarization is additionally revealed along with significant piezoelectric properties, endowing them as promising candidates in the area of photovoltaic solar cells, optoelectronic materials and field effect transistors.