Benefiting from the high voltage and high capacity, transition metal (TM) layered oxides LiNi_1-x-yCo_xMn_yO₂ (NCM) constitute a very attractive family of compounds for the positive electrode of Li-ion batteries. Full quantum simulations such as density functional theory (DFT) method have provided many accurate atomic and electronic structure information, but these understanding is limited to a very small system size of 100-1000 atoms. For micro-scale structures simulations, e.g., multiple phases and interfaces in-between, a large-scale simulation method that can simulate 1000-10000 atoms is required. However, high challenges are faced to develop such method for cathode materials, due to the complex TM-O bonding nature with both ionic and covalent components, the diverse interactions in a quinary system, and the continuous charge state variations during delithiation. In this work, we have developed a multi-scale simulation method for NCM cathode materials, based on Charge-Transfer Modified Embedded-Atom Method (CT-MEAM), in which both the long range Coulomb interaction due to charge transfer and the short range non-ionic interaction can be well described. Properties derived from this method match quite well with the corresponding DFT reference work and essential atomic structure behaviors have been modeled, including NCM interfaces, defect structures, size effects, and corresponding TM distribution interactions, etc. The presented simulation method can help facilitate large-scale atomic calculations required for the optimal design of NCM oxides applications.