We succeeded in growing a high-quality single-crystal of CeAu2Si2, which was previously reported to be highly sample-dependent in terms of electrical and magnetic properties. CeAu2Si2 is not a simple AF1-type anti ferromagnet. but reveals three antiferromagnetic transitions in a narrow temperature range from the Neel temperature T-N1 = 9.6 K to T-N3 = 8.0 K. A clear metamagnetic transition with two steps was observed at H-c1 = 53 kOe and H-c2 = 55 kOe in the magnetization curve below 5 K for the magnetic field along an anti ferromagnetic easy-axis, namely, the tetragonal [001] direction, with a saturation moment of 1.53 mu B/Ce. The magnetic susceptibility and magnetization are anisotropic, which are well explained by results of crystalline electric field analyses. We also studied the de Haas-van Alphen (dHvA) effect. The detected dHvA branches are found to be consistent with those of a non-4f reference compound such as YCu2Si2.