The intermediate-band solar cell (IBSC) has been proposed as a high-efficiency solar cell because of the extended absorption it allows for, which results from the intermediate band. In order to further increase the efficiency of IBSCs, we study a novel device with dual intermediate bands. Because of the extended absorption from the second intermediate band, the efficiency of a dual IBSC can reach 86.5% at a full concentration. Moreover, we study the performance of the IBSC based on InAs/InGaAs quantum dots. The efficiency of the device is shown to be able to reach 74.4% when the In composition is 75%. In addition, the transition process between the dual intermediate bands greatly affects the efficiency, so it is important to design the dual intermediate bands in a precise manner.