Disclosed is an apparatus and method for recovery of target gas, which may increase a target gas concentration in a recovered gas by using a single gas separation membrane module and a plurality of gas storage tanks. The apparatus for recovery of target gas includes a gas separation membrane module configured to perform an enrichment process n times (n is a natural number) so that an injected gas is separated into a permeated gas and a recovered gas in each enrichment process, and (n+1) number of gas storage tanks, wherein in an nth enrichment process, gas stored in an nth gas storage tank is supplied to the gas separation membrane module and separated into an nth permeated gas and an nth recovered gas, the nth permeated gas is stored in a (n−1)th gas storage tank, and the nth recovered gas is stored in a (n+1)th gas storage tank.