Accurate knowledge of electron-ion energy relaxation plays a vital role in non-equilibrium dense plasmas with widespread applications such as in inertial confinement fusion, in laboratory plasmas, and in astrophysics. We present a theoretical model for the energy transfer rate of electron-ion energy relaxation in dense plasmas, where the electron-ion coupled mode effect is taken into account. Based on the proposed model, other simplified models are also derived in the approximations of decoupling between electrons and ions, static limit, and long-wavelength limit. The influences of dynamic response and screening effects on electron-ion energy relaxation are analyzed in detail. Based on the models developed in the present work, the energy transfer rates are calculated under different plasma conditions and compared with each other. It is found that the behavior of electron screening in the random phase approximation is significantly different from the one in the long-wave approximation. This difference results in an important influence on the electron-ion energy relaxation and temperature equilibration in plasmas with temperature $T_{\rm{e}} < T_{\rm{i}}$. The comparison of different models shows that the effects of dynamic response, such as dynamic screening and coupled-mode effect, have stronger influence on the electron-ion energy relaxation and temperature equilibration. In the case of strong degeneracy, the influence of dynamic response will result in an order of magnitude difference in the electron-ion energy transfer rate. In conclusion, it is crucial to properly consider the finite-wavelength screening of electrons and the coupling between electron and ion plasmonic excitations in order to determine the energy transfer rate of electron-ion energy relaxation in dense plasma.