Inclusive bb production in two-photon collisions is studied with the L3 detector at LEP, using 683 pb−1 of data collected at centre-of-mass energies from 183 to 209 GeV. Differential cross sections are determined as functions of the transverse momentum and pseudorapidity of the D*± mesons in the kinematic region 1 GeV<12 GeV and |η|<1.4. The cross sections D*± in this kinematical region is measured and the D*± cross section is derived. The measurements are compared with next-to-leading order perturbative QCD calculations.