Precision instruments are subject to vibration and shock from three axial directions during long-distance transportation and are easily damaged. A suitable three-dimensional vibration isolation platform is required to reduce the impact of precision instruments. The magnetorheological damper has high reliability, low energy consumption, and good vibration damping characteristics and is widely applied in various vibration isolation platforms. To isolate the vibration and shock, a 3-RPC parallel vibration isolation platform based on magnetorheological dampers was designed and its vibration isolation performance was studied. The parallel configuration of 3-RPC was analyzed theoretically and then verified by using the K-G formula. The stress distribution of the hinge and the vibration isolation performance of the whole platform were studied through dynamic simulation. Finally, the vibration isolation performance of the 3-RPC parallel vibration isolation platform prototype was tested by a sine sweep test rig. The experimental results showed that the average vibration transmission rates within 5-60Hz in the X, Y, and Z directions were 39.4%, 46.3%, 71.7%, respectively, which indicated that the 3-RPC parallel vibration isolation platform shall have promising aspects on the vibration and shock isolation of precision instruments.