We have investigated aggregate structures and rheological properties of a colloidal dispersion composed of ferromagnetic spherocylinder particles with a magnetic moment along the particle axis direction, by means of Brownian dynamics simulations. In concrete, we have attempted to clarify the influences of the flow field, magnetic field strength, magnetic interactions between particles and volumetric fraction of particles. In order to discuss quantitatively the internal structures of clusters, we have concentrated our attention on the radial distribution and orientational distribution functions. The present results are compared with those of the theoretical analysis for dilute dispersions and also non-dilute dispersions; the results for the latter were obtained by means of the mean-field approximation, which magnetic particle-particle interactions can be taken into account. Some important results are summarized as follows. For the case of the magnetic field strength and magnetic interactions between particles are more dominant than the viscous forces due to a simple shear flow, chain-like like clusters are formed along the magnetic field direction, although they are slightly tilted to the flow direction. When magnetic particle-particle interactions become over a certain value, such cluster formation leads to a significant increase in the viscosity of the dispersion.