  In this paper, we study the second order Sobolev regularity of solutions to
the parabolic $p$-Laplace equation. For any $p$-parabolic function $u$, we show
that $D(|Du|^{\frac{p-2+s}{2}}Du)$ exists as a function and belongs to
$L^{2}_{\text{loc}}$ with $s>-1$ and $1<p<\infty$. The range of $s$ is sharp.
