  We study the accretion process in the thin disk around a rotating non-Kerr
black hole with a deformed parameter and an unbound rotation parameter. Our
results show that the presence of the deformed parameter $\epsilon$ modifies
the standard properties of the disk. For the case in which the black hole is
more oblate than a Kerr black hole, the larger deviation leads to the smaller
energy flux, the lower radiation temperature and the fainter spectra luminosity
in the disk. For the black hole with positive deformed parameter, we find that
the effect of the deformed parameter on the disk becomes more complicated. It
depends not only on the rotation direction of the black hole and the orbit
particles, but also on the sign of the difference between the deformed
parameter $\epsilon$ and a certain critical value $\epsilon_{c}$. These
significant features in the mass accretion process may provide a possibility to
test the no-hair theorem in the strong field regime in future astronomical
observations.
