  In this paper, we mainly prove a congruence conjecture of Z.-W. Sun
\cite{Sjnt}: Let $p>5$ be a prime. Then $$
\sum_{k=(p+1)/2}^{p-1}\frac{\binom{2k}k^2}{k16^k}\equiv-\frac{21}2H_{p-1}\pmod{p^4},
$$ where $H_n$ denotes the $n$-th harmonic number.
