The present invention relates to a mesoporous molecular sieve MPL-1 and its preparation process. The anhydrous composition of this molecular sieve contains at least three elements, i.e. aluminum, phosphorus and oxygen. The molecular sieve has larger pore diameters, generally 1.3 nm-10.0 nm, a larger specific surface area and adsorption capacity. It is synthesized under the hydrothermal process with an organic compound as template. Where necessary, silicon and/or titanium may be added to synthesize the aluminosilicophosphate, aluminotitanophosphate, or aluminosilicotitanophosphate molecular sieves having a mesoporous structure, and/or metal compounds may be added to synthesize derivatives of mesoporous aluminophosphate molecular sieves containing the corresponding hetero-atoms.