When the induction motor (IM) is used under voltage unbalance，the undesirable effects in the IM occur by the unbalanced phase current. Those are torque reduction，efficiency reduction，vibrating torque，and abnormal temperature rise，etc. So，it is very important to properly protect the IM by motor relay (3E Relay). In this paper，we propose the analysis method on the open phase operation of 3E relay under voltage unbalance. To develop the analysis method，we take into consideration of the unbalanced impedances caused by asymmetry of IM and the open phase operation characteristics of 3E Relay. The unbalanced impedances are identified by measuring various amounts of IM at the state of two different voltage unbalance. The open phase operation characteristics of 3E Relay are clarified by the voltage unbalance tests. The calculation values by the proposed method are the good agreement with the measured value. We clarify the mechanism of the open phase operation of 3E Relay.