The exploration of new monolayer materials always attracts much attention due to the extraordinary properties and promising applications. Here we predict two monolayered aluminum triphosphides (AlP3) with C2/m and P3m1 space groups with a tunable bandgap under strain as the new members of the 2D XP3 family by using the first principles calculations. The stabilities of the predicted structures are confirmed with the phonon dispersion curves and molecular dynamics. Unlike the narrow bandgaps of the reported XP3 monolayers, the larger bandgaps of 1.78 (HSE06) or 1.91 eV (G0W0) for C2/m and 1.42 (HSE06) or 2.14 eV (G0W0) for P3m1 AlP3 monolayers are observed. The high mobility of 1.01 × 105 and 1.62 × 104 cm2 V-1 s-1 are observed for the electron of P3m1 and the hole of C2/m. The optical absorptions of the AlP3 monolayers, in particular, the one with C2/m, are obviously strong in the visible light range. These results imply that the monolayers are promising in the optoelectronic application. Unfortunately, the undesirable band edges make them not suitable for water splitting in spite of the strong optical absorption coefficient in the visible light range. However, an obvious effect of strain engineering is demonstrated for the monolayers. Under -2% and -3% biaxial strain, the band edges of P3m1 AlP3 can straddle the redox potential of water and meet the requirement of photocatalytic water splitting. Therefore, the P3m1 AlP3 monolayer can also be a promising candidate for the photocatalytic water splitting to produce hydrogen driven by the visible light.