A novel rnultiphysics model is, developed in this paper for simulation of the responsive behavior of the magnetic-sensitive hydrogel, with the effects of magneto-chemo-mechanical coupled fields, which is termed the multi effect-coupling magnetic-stimulus (MECm) model. In this work, the magnetic susceptibility for magnetization of the general magnetic hydrogel is defined as a function of finite deformation, instead of a constant for an ideal magnetic hydrogel. The present constitutive equations, formulated by the second law of thermodynamics, account for the effects of the chemical potential, the externally applied magnetic field, and the finite deformation. In particular, a novel free energy density is proposed with consideration of the magnetic effect associated with finite deformation, instead of volume fraction. After examination with published experimental data, it is confirmed that the MECm model can well capture the responsive behavior of the magnetic hydrogel, including the deformation and its instability and hysteresis under 4 uniform or nonuniform magnetic field. The parameter studies are then carried out for influences of the magnetic and geometric properties, including the magnetic intensity, shear modulus, and volume fraction of the magnetic particles, on the behavior, of the Magnetic hydrogel, for a deeper insight into the fundamental mechanism of the magnetic hydrogels.