The s-enhanced and very metal-poor star CS 30322-023 shows a puzzling abundance pattern of the neutron-capture elements, i.e. several neutron-capture elements such as Ba, Pb etc. show enhancement, but other neutron-capture elements such as Sr, Eu etc. exhibit deficient with respect to iron. The study to this sample star could make people gain a better understanding of s- and r-process nucleosynthesis at low metallicity. Using a parametric model, we find that the abundance pattern of the neutron-capture elements could be best explained by a star that was polluted by an AGB star and the CS 30322-023 binary system formed in a molecular cloud which had never been polluted by r-process material. The lack of r-process material also indicates that the AGB companion cannot have undergone a type-1.5 supernova, and thus must have had an initial mass below 4.0M$_odot$, while the strong N overabundance and the absence of a strong C overabundance indicate that the companions initial mass was larger than 2.0M$_odot$. The smaller s-process component coefficient of this star illustrates that there is less accreted material of this star from the AGB companion, and the sample star should be formed in the binary system with larger initial orbital separation where the accretion-induced collapse (AIC) mechanism can not work.