The invention discloses a dealumination Y-type molecular sieve and a preparation method thereof. The crystal cell constant of the ealumination Y-type molecular sieve is 2.430-2.450 nanometers. the relative crystallization degree is more than 65%, pore volume of secondary pore is 0.1-0.3 mL/g, by metering with an oxide, the content of an alkali metal element is less than 0.2 weight%, and the number of non-frame work aluminum in unit crystal cell is less than 3. The invention also discloses a carrier containing the dealumination Y-type molecular sieve and an application and a catalyst containing the carrier and a preparation method and an application thereof. The invention further discloses a hydrocracking method by employing the catalyst. The molecular sieve has high crystallization degree and abundant secondary pore, and lower non-frame work aluminum content, and the catalyst containing the dealumination Y-type molecular sieve can obtain a good balance between activity, intermediate distillate oil selectivity and tail oil BMCI.