This invention relates to a class of microporous metal-silicoaluminophosphate molecular sieves(MeAPSOs) and the method of their fast preparation. These molecular sieves can be represented by the empirical formula on an anhydrous basis: mR· (M q Si x AI y P z )O 2 , wherein "R" represents the templating agent presented in the intracrystalline pore system; " m " is the molar amount of "R" per mole of (M q Si x Al y P z O 2 and has a value from 0.01 to 8.00; "M" represents at least one metal element; " q ", " x ", " y " and " z " represent the molar fractions of metal, silicon, aluminum and phosphorus respectively, whose variations are q=0∼0.98, x=0∼0.98, y=0.01∼0.60, z=0.01∼0.60 and q+x+y+z=1. The crystallization time of the synthesis is 0.5-12 hours, which is defined as the method of fast preparation. This molecular sieve can be used as adsorbents and catalysts of many hydrocarbon conversion processes.