The conversion efficiency of double-clad Raman fiber laser is limited by the cladding-to-core area ratio. To get high conversion efficiency, the inner-cladding-to-core area ratio has to be less than about 8, which limits the brightness enhancement. To overcome the problem, a cascaded-cladding-pumped cascaded Raman fiber laser with multiple-clad fiber as the Raman gain medium is proposed. A theoretical model of Raman fiber amplifier with multiple-clad fiber is developed, and numerical simulation proves that the proposed scheme can improve the conversion efficiency and brightness enhancement of cladding pumped Raman fiber laser.