The invention relates to an air separation system of pressure swing adsorption by secondary adsorption. The air separation system of pressure swing adsorption can further enhance the purity of purified air in a gas storage tank; the technical proposal is that the separation system of pressure swing adsorption of secondary adsorption comprises an adsorption tower, an air inlet device arranged at the inlet opening of the adsorption tower via a pipeline, the inlet opening of the adsorption tower is also connected with an atmospheric desorption device; the outlet end of the adsorption tower is connected with an electric control valve and an one-way valve in parallel and is further connected with a separation air storage tank in series, and the outlet of the separation air storage tank is connected with a stop valve; a molecule screen is positioned in the separation air storage tank. The volume of the separation air storage tank is less than or equal to half of the volume of the adsorption tower; moreover, as the molecule screen is arranged in the purified air storage tank, impure air containing in pure oxygen or nitrogen air after one-time adsorption of the adsorption tower is further adsorbed, leading the purity of the pure oxygen or nitrogen air in the adsorption tower to be further enhanced, thus solving the problems that are not effectively solved for a long time.