Monometallic and bimetallic core-shell nanoparticles (MCSNPs and BCSNPs) exhibit excellent stability, electronic, magnetic and the surface chemical properties due to their combination of metallicity and unique core-shell structure. BCSNPs further has synergistic effects. In this study, we systematically studied the geometrical structure, stability, charge transfer, electronic, and magnetic properties of the 13-, 33- and 55-atom Ni-Ru CSNPs using the density functional theory (DFT) calculations. The results show that Ru@Ni BCSNPs with a Ni surface shell are thermodynamically more favorable than the Ni@Ru BCSNPs with a Ru surface shell. Bader charge analysis illustrates that the Ru surface shell of the Ni@Ru BCSNPs displays a negative charge, while the Ni surface shell of the Ru@Ni BCSNPs exhibits a positive charge or approximately electrically neutral. Charge transfer leads to the shift of the d-band centers and further affects the reactivity. Ru@Ni and Ni@Ru BCSNPs have a higher chemical activity than the corresponding Ni or Ru MCSNPs except Ni@Ru-12. In addition, the Ni@Ru BCSNPs have significantly stronger magnetism when the Ru atoms segregate on surface region. For the MCSNPs of Ru, the size of the particles has an impact on their total magnetic moments.