A method for production of butene-1 by separating C4 olefins from a mixture gas composed of C4 olefins/paraffins via displacement desorption with desorbents and then distilling the separated C4 olefins, in an apparatus including an adsorption facility composed of three adsorption towers (AD-1, AD-2, AD-3) loaded with adsorbents which adsorb olefins selectively and two distillation towers which are one distillation tower for the separation of olefins/desorbents and another distillation tower for the separation of paraffins/desorbents, and a distillation tower for obtaining butene-1 by distilling C4 olefins produced from the adsorption facility, the method comprising: an adsorption process including an adsorption step to introduce the mixture gas of C4 olefins/paraffins into the adsorption towers (AD-1, AD-2, AD-3) loaded with olefin selective adsorbent to adsorb olefins on the adsorbents, discharge non-adsorbed paraffins and the desorbents retained in the adsorption tower to the distillation tower for separation of paraffins and the desorbents through the outlet of the adsorption towers (AD-1, AD-2, AD-3); a C4 olefin rinse step to remove a small amount of paraffins adsorbed together with olefins on the adsorbents by introducing a portion of high purity C4 olefins resulting from the distillation process of olefins/desorbents into the adsorption towers (AD-1, AD-2, AD-3) after the completion of the adsorption step and thus increasing the purity of olefins; a desorption step of obtaining high purity olefins by introducing desorbents into the adsorption towers (AD-1, AD-2, AD-3) after the completion of the rinse step to desorb the C4 olefins and introduce the olefins/desorbents mixture to the distillation tower for the separation of the olefins and the desorbents; and a distillation process for production of butene-1 by distilling the C4 olefins obtained in the adsorption process, wherein said sequential adsorption, olefin rinse and desorption steps are repeatedly performed in each of the adsorption towers (AD-1, AD-2, AD-3), and wherein each of the adsorption towers (AD-1, AD-2, AD-3) is operated to perform a different step with respect to each other at the same time. an adsorption process including an adsorption step to introduce the mixture gas of C4 olefins/paraffins into the adsorption towers (AD-1, AD-2, AD-3) loaded with olefin selective adsorbent to adsorb olefins on the adsorbents, discharge non-adsorbed paraffins and the desorbents retained in the adsorption tower to the distillation tower for separation of paraffins and the desorbents through the outlet of the adsorption towers (AD-1, AD-2, AD-3); a C4 olefin rinse step to remove a small amount of paraffins adsorbed together with olefins on the adsorbents by introducing a portion of high purity C4 olefins resulting from the distillation process of olefins/desorbents into the adsorption towers (AD-1, AD-2, AD-3) after the completion of the adsorption step and thus increasing the purity of olefins; a desorption step of obtaining high purity olefins by introducing desorbents into the adsorption towers (AD-1, AD-2, AD-3) after the completion of the rinse step to desorb the C4 olefins and introduce the olefins/desorbents mixture to the distillation tower for the separation of the olefins and the desorbents; and a distillation process for production of butene-1 by distilling the C4 olefins obtained in the adsorption process, wherein said sequential adsorption, olefin rinse and desorption steps are repeatedly performed in each of the adsorption towers (AD-1, AD-2, AD-3), and wherein each of the adsorption towers (AD-1, AD-2, AD-3) is operated to perform a different step with respect to each other at the same time.