  We report the strength of seed magnetic flux of accretion disk surrounding
the PopIII stars. The magnetic field in accretion disk might play an important
role in the transport of angular momentum because of the turbulence induced by
Magneto-Rotational Instability (MRI). On the other hand, since the primordial
star-forming clouds contain no heavy elements and grains, they experience much
different thermal history and different dissipation history of the magnetic
field in the course of their gravitational contraction, from those in the
present-day star-forming molecular clouds. In order to assess the magnetic
field strength in the accretion disk of PopIII stars, we calculate the thermal
history of the primordial collapsing clouds, and investigate the coupling of
magnetic field with primordial gas. As a result, we find that the magnetic
field strongly couple with primordial gas cloud throughout the collapse, i.e.
the magnetic field are frozen to the gas as far as initial field strength
satisfies $ B\lesssim 10^{-5}(n_{\rm H}/10^3{\rm cm^{-3}})^{0.55}{\rm G}$.
