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 $Hparallel c$ 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 $Hparallel ab$, 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.
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