The invention relates to a metal aluminum-silicon phosphate molecular sieve MeAPSO-41; the water-free chemical formula of the molecular sieve is nMe(SixAlyPz)O2, wherein, n is the mole number of the metal corresponding to the (SixAlyPz)O2 per mole, and x, y and z respectively represent the molar fraction of silicon atom, aluminum atom and phosphorous atom, and n is equal to 0.001 to 0.60, x is equal to 0.001 to 0.60, y is equal to0.001 to 0.70, z is equal to 0.001 to 0.70, and x plus y plus z is equal to 1. The MeAPSO-41 molecular sieve has good water heating stability, and can be used as the ion exchanging agent and the absorption agent, and also can be used for catalyzing the transforming reaction of the hydrocarbon. The molecular sieve is synthesized in the method: aluminum source, silicon source, phosphorous source and the template agent are mixed to gel; AFO structural molecular sieve is adopted as the inoculating crystal; the mixture is heated in the water and crystallized more than one hour at the temperature of 110 to 250 DEG C; during the crystallization process, the mixture is added with metal oxide to produce the reaction compound with the mole compositions of aR2:Al2O3:bP2O5:cSiO2:dMeOx:eH2O, wherein, a is equal to 0.05 to 2.5, b is equal to 0.1 to 2.0, c is equal to 0.01 to 1.5, d is equal to 0.01 to 1.0 and e is equal to 5 to 150; after the crystallization is completed, the product is recycled. The method has simple flow procedures, consumes less template and has low cost.