The invention provides a catalyst for catalytic decomposition of nitrates, nitrites or dilute nitric acid and preparation and application of the catalyst. The preparation method comprises the following steps: (1) roasting and grinding ZSM-5 molecular sieve to obtain HZSM-5 molecular sieve powder; and (2) mixing the obtained HZSM-5 molecular sieve powder with an additive, conducting uniform stirring and molding, and conducting drying and roasting to obtain the catalyst, wherein the additive comprises activated carbon powder, and the mass ratio of the HZSM-5 molecular sieve powder to the activated carbon powder is 2.0:0.5-2.0:4.0. The method for catalytically decomposing nitrates by using the molecular sieve catalyst comprises the following steps that under the atmosphere of nitrogen, one ormore of a nitrate aqueous solution, a nitrite aqueous solution or a dilute nitric acid aqueous solution are subjected to catalytic reduction reaction in a fixed bed reactor through a catalyst bed layer, wherein the catalyst bed layer is filled with the molecular sieve catalyst for catalytically decomposing nitrates. The catalytic decomposition method of the invention is simple, low in cost, capable of reducing environmental pollution and improving economic benefits, and can be used for repairing environmental functions.