  In this paper, we consider the explicit bound for the second-order
approximation of the quadratic variation of a general fractional Gaussian
process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the
covariance function $ R(t,\, s)=\mathbb{E}[G_t G_s]$ can be decomposed into two
parts, one of which coincides with that of fractional Brownian motion and the
other of which is bounded by $(ts)^{H-1}$ up to a constant factor. This
condition is valid for a class of continuous Gaussian processes that fails to
be self-similar or have stationary increments. %Some examples include the
subfractional Brownian motion and the bi-fractional Brownian motion.
  Under this assumption, we obtain the optimal Berry-Ess\'{e}en bounds when
$H\in (0,\,\frac23]$ and the upper Berry-Ess\'{e}en bounds when $H\in
(\frac23,\,\frac34]$. As a by-product, we also show the almost sure central
limit theorem (ASCLT) for the quadratic variation when $H\in (0,\,\frac34]$.
The results extend that of \cite{NP 09} to the case of general Gaussian
processes, unify and improve the Berry-Ess\'{e}en bounds in \cite{Tu 11},
\cite{AE 12} and \cite{KL 21} for respectively the sub-fractional Brownian
motion, the bi-fractional Brownian motion and the sub-bifractional Brownian
motion.
