Laser-driven ion acceleration potentially offers a compact, cost-effective alternative to conventional accelerators for scientific, technological, and health-care applications. A novel scheme for heavy ion acceleration in near-critical plasmas via staged shock waves driven by intense laser pulses is proposed, where, in front of the heavy ion target, a light ion layer is used for launching a high-speed electrostatic shock wave. This shock is enhanced at the interface before it is transmitted into the heavy ion plasmas. Monoenergetic heavy ion beam with much higher energy can be generated by the transmitted shock, comparing to the shock wave acceleration in pure heavy ion target. Two-dimensional particle-in-cell simulations show that quasi-monoenergetic + C 6 ion beams with peak energy 168 MeV and considerable particle number2.1 10 11 are obtained by laser pulses at intensity of1.66 10 20 -W cm 2 in such staged shock wave acceleration scheme. Similarly a high-quality + Al 10 ion beam with a well-defined peak with energy 250 MeV and spread d = E E 30% 0 can also be obtained in this scheme. s e p , where T e is the electron temperature and m p is the proton mass. In addition, the condition for ion reflection, i.e.,