The star HE 1305-0007 is a metal-poor double-enhanced star with metallicity [Fe/H] = -2.0,which is just at the upper limit of the metallicity for the observed double-enhanced stars. Using a parametric model, we find that almost all s-elements were made in a single neutron exposure. This star should be a member of a post-common-envelope binary. After the s-process material has experienced only one neutron exposure in the nucleosynthesis region and is dredged-up to its envelope, he AGB evolution is terminated by the onset of common-envelope evolution. Based on the high radial-velocity of HE 1305-0007,we speculate that the star could be a runaway star from a binary system, in which the AIC event has occurred and produced the r-process elements.