Free vibration characteristics of rectangular composite plate with constrained layer damping and magneto-rheological fluid (MR) core are presented.. Hamilton principal is used to obtain the equation of motion of the sandwich plate. Based on the Navier method, a closed-form solution is presented for free vibration analysis of MR sandwich plate under simply supported boundary conditions. The governing equation of motion is derived on the base of classical lamination theory for the faceplates. Only shear strain energy density of the core is considered. Using displacement continuity conditions at the interface of the layers and core, shear strain of the core is expressed in terms of displacement components of the base and constraint layers. The complex shear modulus of the MR material in the pre-yield region was described by complex modulus approach as a function of magnetic field intensity. The validity of the developed formulation is demonstrated by comparing the results in terms of natural frequencies with those in the available literature. The effects of magnetic field intensity, plate aspect ratio, thicknesses of the MR core, base layer and constrained layer for three different stacking sequences of composite faceplates on the fundamental frequency and loss factor of the first mode are discussed. The results indicate significant effect of physical and geometrical parameters on the natural frequency and loss factor associated with the first mode.