A method for synthesizing a nano SAPO-34 molecular sieve, and an SAPO-34 molecular sieve catalyst and application thereof. A nano SAPO-34 molecular sieve is synthesized by adding a microporous templating agent and a templating agent having a functionalized organic silane to hydrothermal synthesis. The nano SAPO-34 molecular sieve is calcined to obtain a nano SAPO-34 molecular sieve catalyst. The catalyst can be used in a reaction for preparing low-carbon olefin from an oxygen-containing compound. The nano SAPO-34 molecular sieve obtained by this method has a pure CHA crystal phase. Moreover, the nano SAPO-34 molecular sieve catalyst obtained by this method has good catalytic performance in a MTO reaction, the service life of the catalyst is significantly prolonged, and the selectivity of the low-carbon olefin is improved.