  We report the measurements of anisotropic magnetization and magnetoresistance
on single crystals of EuFe$_2$As$_2$, a parent compound of ferro-arsenide
high-temperature superconductor. Apart from the antiferromagnetic (AFM)
spin-density-wave transition at 186 K associated with Fe moments, the compound
undergoes another magnetic phase transition at 19 K due to AFM ordering of
Eu$^{2+}$ spins ($J=S=7/2$). The latter AFM state exhibits metamagnetic
transition under magnetic fields. Upon applying magnetic field with $H\parallel
c$ at 2 K, the magnetization increases linearly to 7.0 $\mu_{B}$/f.u. at
$\mu_{0}H$=1.7 T, then keeps at this value of saturated Eu$^{2+}$ moments under
higher fields. In the case of $H\parallel ab$, the magnetization increases
step-like to 6.6 $\mu_{B}$/f.u. with small magnetic hysteresis. A metamagnetic
phase was identified with the saturated moments of 4.4 $\mu_{B}$/f.u. The
metamagnetic transition accompanies with negative in-plane magnetoresistance,
reflecting the influence of Eu$^{2+}$ moments ordering on the electrical
conduction of FeAs layers. The results were explained in terms of
spin-reorientation and spin-reversal based on an $A$-type AFM structure for
Eu$^{2+}$ spins. The magnetic phase diagram has been established.
