The spin-selective transport through helical molecules has been a hot topic in condensed matter physics, because it develops a new research direction in spintronics, emph{i.e.}, chiro-spintronics. Double-stranded DNA (dsDNA) molecules have been considered as promising candidates to study this topic, since the chiral-induced spin selectivity (CISS) effect in dsDNA was observed in experiment. Considering that the dsDNA molecules are usually flexible in mechanical properties, vibration may be one of important factors to influence the CISS effect. Here, we investigate the influences of electron-vibration interaction (EVI) on the spin-selective transport in dsDNA molecules. We uncover that the EVI not only enhances the CISS effect and the spin polarization ($P_s$) in dsDNA, but also induces a series of new spin-splitting transmission modes. More interesting, these vibration-induced transmission spectra tend to host the same $P_s$ values as those of the original spin-splitting transmission modes, making the $P_s$ spectra to display as a continuous platform even in the energy gap. Our work not only provides us a deep understanding into the influence of vibrations on the CISS effect in helical molecules, {but also puts forwards a feasible route to detect the vibration-induced spin-polarized transport in low-dimensional molecular systems
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