Einstein-Gauss-Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein-Gauss-Bonnet gravity in various spacetime dimensions with both positive and negative couping constant $alpha$. By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $alpha>0$, in $Dgeqslant6$ cases, the black holes will be completely evaporated in a finite time, which resembles the Schwarzschild-AdS case in Einstein gravity. While in $D=4,5$ cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $alpha>0, D=4,5$ will solve the terminal temperature divergent problem of the Schwarzschild-AdS case. For $alpha<0$, in all dimensions, the black hole will always spend a finite time to a minimal mass corresponding to the smallest horizon radius $r_{min}=sqrt{2|alpha|}$ which coincide with an additional singularity. This implies that there may exist constraint conditions to the choice of coupling constant.
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