The invention discloses a catalyst for recycling sulfur and nitrogen in a desulfurization and denitration process absorption solution by a magnesium technology, and a preparation method and an application thereof. The catalyst comprises a carrier, and main active components and cocatalysts, which are supported on the carrier; the carrier is an SBA-15 molecular sieve; the main active components aretransition metals Mn and Co; the cocatalysts comprise a rare earth metal Ce and an alkaline earth metal Ca; the load capacity of the main active components is 0.1-10% of the total weight of the catalyst; and the load capacity of the cocatalysts is 0.1-1% of the total weight of the catalyst. The scaling and blocking problems caused by too high concentration of magnesium sulfite in the desulfurization system are effectively solved, the energy consumption of the traditional desulfurization oxidation system is effectively reduced, the quality of byproducts is improved, the economical property isenhanced, the secondary pollution problem of the catalyst is solved, the recycling of the solid phase catalyst is achieved, and the process cost is greatly reduced.