Modelling the amplitude, frequency and magnetic dependency of magneto-sensitive (MS) rubber in one dimensional case under shear deformation is proposed in this paper. MS rubber is a kind of smart materials which mainly consists of magnetizable particles and rubber matrix. The modulus of MS rubber changes rapidly after the applying of magnetic field which is referred as the magnetic dependency of MS rubber. Besides the magnetic dependency, there is an amplitude and frequency dependency of MS rubber. Specifically, the shear modulus of MS rubber under larger strain magnitude is smaller than the corresponding modulus under small strain and the shear modulus of MS rubber increases with increasing of frequency. A one-dimensional constitutive model consists of a fractional derivative element in parallel with a nonlinear kinematic elastoplastic model to depict the amplitude, frequency and magnetic dependency of MS rubber is developed in this paper. After comparison with the test result, it found that with eight parameters the amplitude, frequency and magnetic dependency can be depict precisely by the model developed. It is helpful for the predicting the dynamic behaviours of MS rubber-based vibration devices in the design phase and promotes MS rubber's application in sound and vibration area.