The influences of an external magnetic field and a simple shear flow on rheological properties of colloidal dispersions composed of ferromagnetic rod-like particles were investigated by means of Brownian dynamics simulations. The ferromagnetic rod-like particles were modeled as a spherocylinders with magnetic charges on each hemisphere of the particles. The external magnetic field was applied along the direction normal to the shear plane. The net viscosity was decomposed into three components for detailed discussion: these three viscosity components arise from (a) the torque due to the magnetic particle-field interaction, and (b) the torque and (c) the force due to the interaction between particles. The main results were as follows. Under a relatively weak shear flow field, the viscosity increases significantly with increasing the magnetic particle-particle interaction. This is because chain-like clusters formed in the direction of the field induce a large resistance in a flow field. In contrast, when the flow field is dominant, the strong flow field collapses the chain-like clusters and the viscosity decreases.