In this paper, we present a design method of broadband reflective circular polarizer (BRCP) in the extreme ultraviolet (EUV) region. By using this method, we designed three BRCPs with a 6, 12 and 18 eV bandwidth, respectively. Then, we investigated the performances of designed BRCPs in theory. The results indicated that the reflected lights of these BRCPs all showed a nearly 100% circular polarization degree and considerable circular reflection in their design band. In addition, we also studied the origin of high circular polarization degree by analyzing the phase shift and the reflectivity ratio between s- and p-polarized lights induced by the reflection of BRCPs. Furthermore, the pulse responses of BRCPs for attosecond pulses were also investigated. The proposed EUV BRCPs can be used for controlling the polarization state of broadband EUV sources, e.g., generating the circularly polarized attosecond pulse by a linearly polarized one.