Problems on catalyst production and catalyst performance with respect to conventional 8-oxygen-membered ring micropore-containing crystalline silicoaluminophosphate molecular sieves as non-equilibrium methylamine synthesis catalysts, are resolved. A chabazite type crystalline silicoaluminophosphate molecular sieve having high purity and high crystallinity and having, on a crystal grain surface, an amorphous oxide layer whose Si/Al atomic ratio is greater than that of the whole crystal grain can be stably produced with high yield with the use of a small amount of structure directing agents by the present method characterized in that hydrothermal treatment conducted in the production of 8-oxygen-membered ring micropore-containing crystalline silicoaluminophosphate sieves is controlled under specified treating conditions. The thickness and composition of the amorphous oxide layer, which exert marked influence on the yield of dimethylamine synthesis, can be easily controlled and reproduced under the conditions of catalyst synthesis according to the invention. Thus, the catalyst of high performance can be stably supplied by the present invention at a low cost with reduced output of waste.