We have investigated the rheological properties and the orientational distributions cof particles of a dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. First, the governing equation of the orientational distribution function has been derived from the balance of the torques acting on the particle in an applied magnetic field. Then, the governing equation has been solved aproximately by Galerkin's method, after the solution was expanded in spherical harmonics. The results obtained here are summarized as follows. The orientational distribution function has a sharper peak for a stronger magnetic field, and the direction of the peask changes from a flow direction to a magnetic field one as the magnetic field comes to govern the shear flow. Since the direction of the particle is highly limited in the field direction as the magnetic field becomes strong, the viscosity increases significantly. The particle of a larger aspect ratio leads to the larger increment in the viscosity, since such elongated particles induce larger resistance in a flow field.