Accurate knowledge of electron-ion energy relaxation plays a vital role in non-equilibrium dense plasmas with wide 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 effects are taken into account. Based on the proposed model, other simplified models have also derived with the introduction of the approximations of decoupling of electrons and ions, static limit as well as long-wavelength limit. Detailed analysis of the influence of dynamic response and screening effects on electron-ion energy relaxation is performed. Using the models developed in the present work, the energy transfer rates under different plasma conditions are calculated and compared. For the screening effect, it is found that the behavior of electron screening based on the random phase approximation is significantly different from the one under the long-wave approximation. This difference have important influence on the electron-ion energy relaxation and temperature equilibration in plasmas with temperature $T_\mathrm{e} < T_\mathrm{i}$. By comparing different models, it is shown that effects of dynamic response such as the dynamic screening and coupled-mode effect have stronger impact on the electron-ion energy relaxation and temperature equilibration. The effect of dynamic response will bring about an order of magnitude difference in the electron-ion energy transfer rate in the case of strong degeneracy. As a conclusion, correctly taking into account the finite-wavelength screening of electrons and the coupling of electronic and ionic plasmon excitation is of essential importance in determining the energy transfer rates for electron-ion energy relaxation in dense plasmas.