Cu3(OH)4SO4, a parallel Cu (S = 1/2) triple chain system, is an interesting magnet because an idle-spin state is expected on the central chain. We have succeeded in growing high-quality single crystals of Cu3SO4(OH)4 by a hydrothermal method from copper sulfate and copper hydroxide. We measured field dependence of the magnetization on a single crystal under various directions of magnetic field up to 7 T. We found a clear magnetic anisotropy and confirmed that the existence of the easy axis lies in the ac plane. Under magnetic fields parallel to the c-axis and the a-axis at 2.5 K, we observed field-induced successive magnetic transitions. In the case of B//c, two anomalies of the magnetization are observed at 0.9 and 1.7 T, On the other hand, there are broad anomalies in the magnetization at 3.7 and 5.6 T in the case of B//a.