In this work behavior of an arbitrarily fiber-reinforced viscoelastic and magneto-sensitive material. is investigated systematically in the frame of modern continuum mechanics when they are subjected to external loadings. The matrix material is supposed to be made of viscoelastic material with magnetic sensitivity involving an artificial anisotropy due to fiber reinforcing by arbitrary distribution. Magneto-viscoelastic response of the material will show up as a stress consisting of a reversible and irreversible parts along with a magnetization field. Magnetic field and elastic stress field is derived from a thermodynamic potential, with the dissipative stress arising as a result of viscous properties of the material. Response functions in regard to objectivity axiom/1/depend in general to Green deformation and rate tensors, magnetic field, fiber distribution and temperature distribution. Constitutive equations for the stress and magnetization with the use of relevant balance equations yields field equations for the formulation and solution of boundary value problems for the bodies made of those materials under considerations.