  Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (0$\leq x \leq$1.00) single crystals
with high-quality have been grown successfully using the travelling-solvent
floating-zone technique. The patterns of X-ray diffraction suggest high
crystalline quality of the samples. After post-annealing in flowing oxygen at
600 $^o$C, the crystals show sharp superconducting transitions revealed by AC
susceptibility. The hole concentration $p$ is deduced from superconducting
transition temperature ($T_c$), which exhibits a linear relation with La doping
level $x$. It ranges from the heavily overdoped regime ($p \approx$ 0.2) to the
extremely underdoped side ($p \approx$ 0.08) where the superconductivity is
absent. Comparing with the superconducting dome in
Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ system, the effects from out-of-plane
disorders show up in our samples. Besides the La doping level $x$, the
superconductivity is also sensitive to the content of oxygen which could be
tuned by post-annealing method over the whole doping range. The post-annealing
effects on $T_c$ and $p$ for each La doping level are studied, which give some
insights on the different nature between overdoped and underdoped regime.
