Barium stars are peculiar stars with enhanced slow neutron capture process (s-process) elements. Abundance analysis of them aids in better understanding the chemical evolution of the Milky Way. In this paper, we introduce a data-driven method named the memory-enhanced adaptive spectral network (MEASNet) to search for barium candidates in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low-resolution survey (LRS) and estimate the abundance of five s-process elements: Sr, Y, Ba, Ce, and Nd. MEASNet, trained using spectra from common stars in both LAMOST and the Galactic Archaeology with HERMES survey, showcases notable performance: for the classification task, precision = 98.22% and recall = 94.12%; in prediction, the mean absolute error for the seven elements range between 0.07 and 0.15 dex. After training, we apply the model to 4,083,003 stellar spectra from LAMOST DR10 LRS, successfully identifying 1,803,670 spectra of barium candidates ([Ba/Fe] ≥ 0.25 dex) along with their five s-process elemental abundances. The catalog enlarges the sample size, providing a wealth of data for further statistical analysis of the formation and evolution of barium stars. Meanwhile, this work highlights the potential value of MEASNet in star classification and abundance estimation, offering a strong reference for future data-driven models.