In this work we calculate the Sunyaev-Zeldovich (SZ) effect due to the $e^+e^-$ from dark matter (DM) annihilation in galaxy clusters. Two candidates of DM particle, (1) the weakly-interacting massive particle (WIMP) and (2) the light dark matter (LD
M) are investigated. For each case, we also consider several DM profiles with and without central cusp. We generally find smaller signals than previously reported. Moreover, the diffusion of electrons and positrons in the galaxy clusters, which was generally thought to be negligible, is considered and found to have significant effect on the central electron/positron distribution for DM profile with large spatial gradient. We find that the SZ effect from WIMP is almost always non-observable, even for the highly cuspy DM profile, and using the next generation SZ interferometer such as ALMA. Although the signal of the LDM is much larger than that of the WIMP, the final SZ effect is still very small due to the smoothing effect of diffusion. Only for the configuration with large central cusp and extremely small diffusion effect, the LDM induced SZ effect might have a bit chance of being detected.
