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We have carried out high magnetic field studies of single-crystallineLi$_2$MnO$_3$, a honeycomb lattice antiferromagnet. Its magnetic phase diagramwas mapped out using magnetization measurements at applied fields up to 35 T.Our results show that it undergoes two successive meta-magnetic transitionsaround 9 T fields applied perpendicular to the ab-plane (along the c*-axis).These phase transitions are completely absent in the magnetization measuredwith field applied along the ab-plane. In order to understand this magneticphase diagram, we developed a mean-field model starting from the correctNeel-type magnetic structure, consistent with our single crystal neutrondiffraction data at zero field. Our model calculations succeeded in explainingthe two meta-magnetic transitions that arise when Li$_2$MnO$_3$ enters twodifferent spin-flop phases from the zero field Neel phase.

Successive spin-flop transitions of Neel-type antiferromagnet Li$_2$MnO$_3$ single crystal with honeycomb-lattice