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