This paper presents the suppression method of anti-resonance and resonance caused by use of air springs, which are the actuator of a pneumatic vibration isolator. Although the relative displacement derivative (RDD) positive feedback control is effective for the suppression of the anti-resonance and resonance, a control system is not causal under the condition that the time delay of response of air springs is present. To overcome this issue, the RDD positive feedback control combined with Smith prediction is used. The effectiveness of the proposed approach is shown by simulation and experiment.