The invention relates to an air source heat pump double-water-tank hot water system and a control method. The air source heat pump double-water-tank hot water system comprises a variable-frequency water supply pump, a hot water tank, a warm water tank and a parallel host which are connected in sequence, and further comprises a water return valve and a water replenishing valve which are connected with the warm water tank; the hot water tank, the warm water tank and the parallel host are sequentially connected to form host-water tank circulation; the warm water tank, the hot water tank, the variable-frequency water supply pump and the water return valve are sequentially connected to form water tank-tail end circulation; and the parallel host comprises a plurality of parallel branches which are independently controlled or not independently controlled, and different heat supply modes are achieved by opening a specific number of parallel branches, so that different tail end load requirements are met. Compared with the prior art, the double-water-tank scheme is adopted, so that the mixing loss among return water, replenished water and hot water is reduced; and meanwhile, the water inlet temperature and the water outlet temperature of the heat pump are reduced, the condensation temperature of the heat pump can be well reduced, and the energy efficiency of the heat pump unit is improved while water consumption of a user is guaranteed.