Single crystals of Bi2Sr2Ca1-xYxCu2O8+z with Y concentration between 0.0 and 0.51 have been prepared by the travelling-solvent-floating-zone method. The composition, structure, superconductivity and critical current density of this system were investigated. Evidence is found that yttrium has substituted the Ca ions, which leads to a linear decrease of c-axis length. However, a second phase is also found for high Y concentration (x>0.2) of which the c-axis length is nearly independent of the composition. The substitution of Ca by Y enhances Tc up to 95.3 K at x=0.2, but depresses Tc sharply for x>0.2. The temperature dependence of Jc(T) shows a kink at about 25 K (± 3 K) for x<0.5, indicating that there exist always two different pinning regimes in the Y-substituted single crystals.