We have investigated the rheological properties and the orientational distributions of particles of a dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The governing equation of an orientational distribution function has been derived from the balance of the torques acting on a particle in an applied magnetic field. After a spherical harmonic expansion, an approximate solution to the governing equation has been found by Galerkin's method. The results obtained are summarized as follows. The orientational distribution function has a sharper peak for a stronger magnetic field, and the position of the peak changes from the flow direction to the magnetic field direction as the magnetic field comes to govern the shear flow. Since the orientation of the particle is highly restricted in the field direction as the magnetic field becomes strong, the viscosity increases significantly. The particles with a larger aspect ratio lead to the larger increment in the viscosity, since they induce a larger resistance in a flow field.