Two-dimensional (2D) structures of BiMP6 (M = Al, Ga, In) are predicted and the dynamical, thermal, and energy stabilities are confirmed. The electronic properties, strain engineering, and mobility are investigated by HSE06, while the absorptions are determined with both HSE06 and GW + BSE. The results demonstrate that the band gaps BiMP6 decrease along with the increase of M atomic numbers. Accordingly, the band edges of BiAlP6 and BiGaP6 can cross the redox potential of water to meet the requirements of water-splitting reaction to produce hydrogen. Moreover, the band edges could be changed under strains but still match the condition of water splitting reaction while the biaxial strain is not too large. The absorptions of all the BiMP6 monolayers are obvious in the visible light region and significantly enhanced by strain. In addition, the carrier mobilities of BiMP6 monolayers are ~105 cm2V−1s and close to the highest one of the reported 2D materials in the literature, which are a benefit for the photocatalytic water splitting reaction and photoelectron applications.