  We perform two-dimensional, axisymmetric, magnetohydrodynamic simulations of
the collapse of a rotating star of 40 Msun and in the light of the collapsar
model of gamma-ray burst. Considering two distributions of angular momentum, up
to \sim 10^{17} cm^2/s, and the uniform vertical magnetic field, we investigate
the formation of an accretion disk around a black hole and the jet production
near the hole. After material reaches to the black hole with the high angular
momentum, the disk is formed inside a surface of weak shock. The disk becomes
in a quasi-steady state for stars whose magnetic field is less than 10^{10} G
before the collapse. We find that the jet can be driven by the magnetic fields
even if the central core does not rotate as rapidly as previously assumed and
outer layers of the star has sufficiently high angular momentum. The magnetic
fields are chiefly amplified inside the disk due to the compression and the
wrapping of the field. The fields inside the disk propagate to the polar region
along the inner boundary near the black hole through the Alfv{\'e}n wave, and
eventually drive the jet. The quasi-steady disk is not an advection-dominated
disk but a neutrino cooling-dominated one. Mass accretion rates in the disks
are greater than 0.01 Msun/sec with large fluctuations. The disk is transparent
for neutrinos. The dense part of the disk, which locates near the hole, emits
neutrino efficiently at a constant rate of < 8 \times 10^{51} erg/s. The
neutrino luminosity is much smaller than those from supernovae after the
neutrino burst.
