The invention relates to an ultrafine grain molecular sieve for the preparation of low-carbon alkene by the petroleum hydrocarbon cracking as well as a catalyst and application thereof. The aperture of the molecular sieve is between 5-6.5, the ratio of silicon to aluminum is 20-1000, and the diameter of grain is 20-900nm; the total acid amount represented by an ammonia temperature programmed desorption method is not more than 0.75mmol/g, and no strong acid peak appears; and the ratio of B acid to L acid, infrared represented with pyridine, is less than 1. When applied to the preparation of low-carbon alkene by the petroleum hydrocarbon cracking, a forming catalyst prepared from the molecular sieve of the invention has the following characteristics that: (1) in comparison with the steam thermal cracking process, higher yield of total weight of ethylene and propylene can be obtained under the temperature lower than the requirement of >= 200 specified in the traditional steam thermal cracking process; meanwhile, the yield of methane is reduced by at least 10 percentage points, and the ratio of propylene to ethylene is increased to more than 1; and (2) in comparison with a catalyst prepared from a conventional grain molecular sieve, the yield of total weight of ethylene and propylene can be increased about more than 10 percentage points under the same reaction conditions.