Large single crystals of the EuCu2Si2 intermetallic compound have been successfully grown by a high pressure vertical floating zone method with optical heating. The suppression of evaporation of volatile elements and control of the floating zone temperature are the key factors for the stability of the growth process. A low travelling velocity of 3 mm/h and a short length of the floating zone play an important role in phase selection and formation of a EuCu2Si2 single crystal. Measurements of oriented single crystalline EuCu2Si2 samples reveal a non-linear temperature dependence of the magnetic susceptibility attributed to the valence fluctuations in Eu ion. But no magnetic ordering transition occurs at T > 2 K. The magnetic susceptibility data display significant anisotropy with a magnetic easy c-axis ([0 0 1]). In contrast to the magnetic susceptibility, the anisotropy in the electrical resistivity for the two different crystallographic orientations is less significant. (C) 2010 Elsevier B.V. All rights reserved.