A process and apparatus for separating an olefin from mixed gases containing light olefins is provided. The process includes adsorbing the olefin of an olefin-containing mixed gas in an adsorption column packed with an adsorbent selectively adsorbing the olefin; discharging gases other than the olefin through the outlet of the adsorption column; desorbing the adsorbed olefin by displacement using a desorbent, and separating the olefin from the desorbent, thereby producing a high-purity olefin. The apparatus includes adsorption columns packed with an adsorbent selectively adsorbing an olefin, and at least two distillation columns for separating an olefin/desorbent mixture and an olefin poor stream/desorbent into their components. If the olefin concentration of the off-gas from an olefin rinse step is higher than that of a raw material gas, recovering the olefin from the off-gas is carried out before or after the adsorption step.