The flux difference splitting (FDS) combined with the characteristic-wise weighted essentially non-oscillatory (WENO) reconstruction in single-component flow simulations is quite attractive and preferred for its better non-oscillatory feature near discontinuities. However, when compressible multi-component flows are simulated, the FDS with the characteristic-wise WENO reconstruction may cause spurious oscillations. In this work, we analyze the reason that the oscillations are generated. A new method, which can effectively suppress this kind of spurious oscillations in multi-component flows, is proposed by modifying the total energy in the process of the WENO reconstruction. For example, in the fifth-order WENO reconstruction, on the global stencil $S^5=(j−2,j−1,···,j+2)$ used to reconstruct the left-side value $U^L_{ j+1/2},$ the total energy values are first modified by using the reconstructed value of the specific heat ratio (i.e., $γ^L_{j+1/2},$ which can be directly reconstructed from the transport equation of the mass fraction), and then the characteristic-wise WENO reconstruction process is implemented. Numerical examples including several one-, two and three-dimensional multi-component flows confirm the effectiveness and robustness of the proposed method.