The poor cycling performance of Li-rich cathode Li₂MnO₃, a promising cathode for next-generation Li-ion batteries, limits its commercial applications. Transition metal (TM) doping is widely applied to optimize the electrochemical performance of Li₂MnO₃, where the d valence electrons of the TM play a crucial role. Nevertheless, the rule of the doping effect of TM with various numbers of d electrons has not been well summarized. In this work, 4d-TMs (Zr, Nb, Mo, Ru and Rh) are selected as dilute doping elements for Li₂MnO₃ to evaluate their effect on the performance of Li₂MnO₃ through first-principles calculations. The calculations indicate that as the number of 4d electrons increases, the doped TM transforms from an electrochemically inert state (Zr and Nb) to an electrochemically active state (Mo, Ru and Rh) in Li₂MnO₃. Meanwhile, the orbital hybridization between the 4d electrons of the TM and the 2p electrons of O becomes stronger from Zr to Rh, which promotes the co-oxidation of the TM and O for charge compensation and alleviates the excessive oxidation of O, thus enhancing the stability of O. Moreover, the oxidation of the doped TM and lattice Mn during charging can trigger a decrease in the initial average delithiation potential. Although the 4d-TMs exhibit slight promoting or inhibiting effects on Li diffusion, no obvious rule related to the number of d electrons has been found. Our work highlights the rule of the doping effect of TMs with different 4d electrons on the electrochemical performance of Li₂MnO₃ and would facilitate a better design of Li₂MnO₃ cathode materials.