  We develop a framework for magnetohydrodynamical (MHD) simulations in a local
cylindrical shearing box by extending the formulation of the Cartesian shearing
box. We construct shearing-periodic conditions at the radial boundaries of a
simulation box from the conservation relations of the basic MHD equations,
taking into account the explicit radial dependence of physical quantities. We
demonstrate quasi-steady mass accretion, which cannot be handled by the
standard Cartesian shearing box model, with an ideal MHD simulation in a
vertically unstratified cylindrical shearing box up to 200 rotations. In this
demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally
isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation,
whereas the sound velocity and the initial Alfven velocity have the same radial
dependence as that of the Keplerian velocity. Inward mass accretion is induced
to balance with the outward angular momentum flux of the MHD turbulence
triggered by the magnetorotational instability in a self-consistent manner. We
discuss detailed physical properties of the saturated magnetic field, in
comparison to the results of a Cartesian shearing box simulation.
