Electrical resistivity and ac-susceptibility measurements under high pressure were carried out in high-quality single crystals of $alpha$-Mn. The pressure-temperature phase diagram consists of an antiferromagnetic ordered phase (0<$P$<1.4 GPa, $T<T_{rm N}$), a pressure-induced ordered phase (1.4<$P$<4.2-4.4 GPa, $T<T_{rm A}$), and a paramagnetic phase. A significant increase was observed in the temperature dependence of ac-susceptibility at $T_{rm A}$, indicating that the pressure-induced ordered phase has a spontaneous magnetic moment. Ferrimagnetic order and parasitic ferromagnetism are proposed as candidates for a possible magnetic structure. At the critical pressure, where the pressure-induced ordered phase disappears, the temperature dependence of the resistivity below 10 K is proportional to $T^{5/3}$. This non-Fermi liquid behavior suggests the presence of pronounced magnetic fluctuation.
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