  The inclusive production of the doubly heavy baryon $\Xi_{bb}$ is
investigated at polarized and unpolar- ized photon collider. bb pair in both
color triplet and sextet have been considered to transform into $\Xi_{bb}$. The
results indicate that the contribution from color sextet is about 8% for
$\Xi_{bb}$ production. For the ILC collision energy ranging from 91GeV to
1000GeV, the total cross section of $\Xi_{bb}$ shows a downtrend, i.e., the
production of $\Xi_{bb}$ has the maximal rate at $\sqrt S = 91GeV$. Our results
indicate that the initial beam polarization may be an important asset for the
production of $\Xi_{bb}$. At some collision point, the production rate of
$\Xi_{bb}$ can be increased about 17% with an appropriate choice of the initial
beam polarization.
