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.
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