Lithium-metal battery based on Ni-rich cathode provides high energy density but presents poor cyclic stability due to the unstable electrode/electrolyte interfaces on both cathode and anode. In this work, we report a new strategy to address this issue. It is found that the cyclic stability of Ni-rich/Li battery can be significantly improved by using succinic anhydride (SA) as an electrolyte additive. Specifically, the capacity retention of LiNi0.8Co0.1Mn0.1O2 (NCM811)/Li cell is improved from 14% to 83% after 200 cycles at 1 C between 3.0 and 4.35 V by applying 5% SA. The underlying mechanism of SA contribution is understood by comparing the effects of malic anhydride (MA) and citraconic anhydride (CA), both of which share a similar molecular structure to SA but show different effects. On anode side, SA can but MA and CA cannot form a protective solid electrolyte interphase (SEI) on Li anode. On cathode side, three anhydrides can suppress the formation of hydrogen fluoride from electrolyte oxidation decomposition, but SA behaves best. Typically, MA shows adverse effects on the interface stability of Li anode and NCM811cathode, which originates from its high acidity. Though the acidity of MA can be mitigated by substituting a methyl for one H atom at its CC bond, the substituent CA cannot compete with SA in cyclic stability improvement of the cell, because the SEI resulting from CA is not as robust as that from SA, which is related to the binding energy of the SEI components. This understanding reveals the importance of the electrolyte acidity on the Ni-rich cathode and the robustness of the SEI on Li anode, which is helpful for rationally designing new electrolyte additives to further improve the cyclic stability of high-energy-density Ni-rich/Li batteries.