We present detailed studies of the enhanced coercivity of exchange-bias bilayer Fe/MnPd, both experimentally and theoretically. We have demonstrated that the existence of large higher-order anisotropies due to exchange coupling between different Fe and MnPd layers can account for the large increase of coercivity in the Fe/MnPd system. The linear dependence of coercivity on inverse Fe thickness is well explained by a phenomenological model by introducing higher-order anisotropy terms into the total free energy of the system.