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This paper reports that high quality CuGeO3 single crystals were successfully grown by floating-zone technique and the magnetic property was studied.The temperature dependence of magnetic susceptibility below the spin-Peierls (SP)transition temperature(Tsp)under magnetic fields applying along both the a-and c-axis direction can be fitted well by a model of noninteracting dimmers.The spin gap derived from the fitting is consistent with other reports.There is a very weak anisotropy in the fitting parameters for different directions,which should be expected from a SP system.A small uptu in susceptibility at low temperature due to paramagnetic impurities and/or defects can be observed.A suppression of the uptu by magnetic field is first discovered in this system and the possible origins for this suppression are discussed.