Semi-active isolators with laminated magnetorheological elastomer (MRE) structures draw increasing attentions for vibration control because of their resonance-frequency-shift property. Their vibration attenuation capacity can be further improved by integrating the acoustic metamaterial characteristics with tunable vibration bandgaps at designed frequencies. On this basis, a novel metamaterial MRE isolator with controllable vibration bandgaps was designed and prototyped. The mechanism of the formation of vibration bandgaps was analysed theoretically using the method of mass-spring model. Both infinite and finite periodic structures were discussed respectively. The equivalent negative stiffness of the metamaterial MRE isolator was studied. The evaluation experiments were conducted to study bandgaps of the metamaterial MRE isolator and its vibration isolation capacity. Results demonstrate that the new metamaterial MRE isolator possesses controllable bandgaps and can provide improved vibration isolation performance.