We have studied superconducting properties of $Mg_{1-x}Al_xB_2$ single crystals from reversible magnetization measurements. It was found that the upper critical fields $H_{c2}$ were decreased for both H // c and H // ab as Al is substituted for Mg. As a result, the large anisotropy of $H_{c2}$ observed in pure $MgB_2$, which is considered as one of the characteristics of two-gap superconductor, was decreased with Al doping. On the other hand, the irreversibility fields $H_{irr}$ were increased for x = 0.1 and were significantly decreased for x = 0.2. In contrary to the anisotropy of $H_{c2}$, the anisotropy of $H_{irr}$ was increased as Al concentration increases.