High-quality Bi2+xSr2-xCuO6+delta (0 < x <= 0.5) single crystals have been grown successfully using the travelling-solvent floating-zone (TSFZ) technique. The samples with x > 0.05 are in the underdoped level. The structure of these crystals was investigated by X-ray diffraction. The evolution of c-axis lattice parameters with varied x is displayed, which is strongly associated with the behavior of T-c. The crystals exhibit superconducting transitions with T-c = 9-0.8 K for the samples with x = 0.05-0.20, while for samples with x = 0.25 and above no superconductivity was discovered down to 1.6 K. The resistivity of samples with x = 0.31, 0.40 and 0.50 exhibits a drastic divergence as temperature approaches 0 K. (C) 2007 Elsevier B.V. All rights reserved.