An AFI-CHA hybrid crystal molecular sieve and an NH3-SCR catalyst using the AFI-CHA hybrid crystal molecular sieve as a carrier, and preparation methods thereof are disclosed. The AFI-CHA hybrid crystal molecular sieve includes an AFI-type SAPO-5 molecular sieve and a CHA-type SAPO-34 molecular sieve, with hybrid crystal grains of AFI and CHA. The hybrid crystal molecular sieve is synthesized by a hydrothermal synthesis method and can be obtained by changing the structure directing agent, the heating rate and the calcinating temperature in the preparation process. Further, copper is loaded on the basis of the hybrid crystal molecular sieve to prepare copper-based NH3-SCR catalyst and corresponding monolithic catalyst. The catalytic activity and hydrothermal stability of the catalyst are significantly improved by the hybrid crystal molecular sieve.