  In this paper we establish a moderate deviation principle of the hitting
times for trajectories of sums of independent and identically distributed
random variables. The main idea of proof is to convert the moderate deviations
over a small time interval into the moderate deviations at a point, then
utilize the moderate deviations for trajectories of sums of independent random
variables given by Hu in \cite{Hu2001} to get the moderate deviations at a
point. By the upper bounds of large deviations for trajectories of sums of
independent random variables given by Schuette in \cite{ Schuette1994}, we can
prove that our convert doesn't influence the rate function of the moderate
deviation.
