  Based on the quasiclassical theory, we investigate the vortex state in a
two-band superconductor with a small gap on a three dimensional Fermi surface
and a large gap on a quasi-two dimensional one, as in MgB_2. The field
dependence of zero-energy density of states is compared for fields parallel and
perpendicular to the ab plane, and the anisotropy of the vortex core shape is
discussed for a parallel field. The Fermi surface geometry of two-bands,
combining the effect of the normal-like electronic state on the small gap band
at high fields, produces characteristic behavior in the anisotropy of c- and
ab-directions.
