A finite element computational technique for predicting the behavior of a compound drop which is composed of the shell and core phases and is suspended stationarily in a continuous phase under the influence of a uniform DC electric field has been developed, and then the effects of the electric field strength and the volume ratio of the core phase to the shell phase on the circulations induced in each phases and the drop deformations have been investigated. The computed results showed the different behavior of the compound drop from that of a single drop due to the existence of the core phase with different physical properties inside the drop.