  We report the ac magnetic susceptibility $\chi_{ac}$ and resistivity $\rho$
measurements of EuFe$_2$As$_2$ under high pressure $P$. By observing nearly
100% superconducting shielding and zero resistivity at $P$ = 28 kbar, we
establish that $P$-induced superconductivity occurs at $T_c \sim$~30 K in
EuFe$_2$As$_2$. $\rho$ shows an anomalous nearly linear temperature dependence
from room temperature down to $T_c$ at the same $P$. $\chi_{ac}$ indicates that
an antiferromagnetic order of Eu$^{2+}$ moments with $T_N \sim$~20 K persists
in the superconducting phase. The temperature dependence of the upper critical
field is also determined.
