We have analyzed the time-dependent behaviors of the orientational distributions of a nondilute colloidal dispersion composed of the ferromagnetic spherocylinder particles influenced by the external magnetic field. In order to understand the effects of the magnetic interactions between the particles, we have derived a series of basic equations for the orientational distributions of the particles in steady three dimensional flow by applying the mean-field theory and the perturbation expansion method. Exact solutions of the basic equations are obtained theoretically. By using the solution, the mean-field, which is derived from the self-consistent condition, is analytically calculated. The magnetic interactions between the particles restrict the particle directions and make the particle incline to the direction of the chainlike cluster.The strength of the restriction decreases with the larger aspect ratio of the particle. Compared with a dilute system, in the nondilute system, the existence of the particle-particle interactions provides the increased stability of the particle orientation and the swift response to the external magnetic field.