A shrouded oscillating-foil turbine is proposed to augment the energy extraction performance. The oscillating foil undergoes combined plunging and pitching motion to convert the flow energy. A diffuser is introduced into the oscillating-foil-based turbine as the shroud. The speed-up and energy extraction performance of the turbine were assessed numerically. The effects of three cost-independent geometrical factors, namely shroud entrance width, shroud angle and streamwise distance between shroud and foil, and shroud sectional shape on energy extraction performance were investigated in detail. The optimal motion parameters for the shrouded oscillating-foil turbine were re-explored due to the altered flow field in the shroud. The results demonstrated that the maximum energy extraction efficiency of bare oscillating foil (0.336) can be augmented by 35.8% to 0.456 by appropriate arrangement of the shroud with a relative chord length of 0.8. The optimal motion parameters for the shrouded foil are slightly different from those of bare foil. The re-tuned motion parameters can further improve the efficiency to 0.47. Considering both the manufacturing cost of the shaped sections and their performance, it is more advantageous and attractive to use a flat plate as the shroud in engineering practices.