  Consider simple random walk on a realization of an Erd\H{o}s-R\'enyi graph.
Assume that it is asymptotically almost surely (a.a.s.) connected. We prove a
Central Limit Theorem (CLT) for the average target hitting time. By the latter
we mean the expected time it takes the random walk on average to first hit a
vertex $j$ when starting in a fixed vertex $i$. The average is taken with
respect to $\pi_i$, the invariant measure of the random walk.
