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An extensive magnetization study in pulsed fields up to 62 T and at temperatures down to ~0.7 K has been performed on the single crystals of hexagonal manganite HoMnO₃. For magnetic fields (<i>H</i>) applied along the <i>c</i>-axis, successive magnetic transitions below 10 T and a step-like transition at ~41 T are observed. The phase diagram for <i>H//c</i> is very complex and new phase boundaries are explored below 6 K. This phase diagram is compared with the early results derived from dielectric constant and neutron scattering measurements. For <i>H//a</i>, two magnetic transitions are found below 3 T dome-shaped and the phase diagram is reported for the first time. The variety of magnetic symmetries of the field-induced magnetic phases is discussed.