  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
