In this paper, we establish various congruences involving harmonic numbers \(H_{3n}\) and \(H_{3n+r}\) modulo prime number p, ie., \(\sum _{0\le k\le [ p/3] }H_{3k}^{2}\pmod {p}\) and \( \sum _{0\le k\le [ p/3] } \frac{H_{3k+r}}{3k+r}\pmod {p}\) . Also, we give the generalization of Meštrović’s congruence, ie., for any prime number \( p\ge 5,\) \(\begin{aligned} \sum _{k\equiv r \pmod {3}}^{p-1}\frac{\left( -1\right) ^{k}}{k}\left( {\begin{array}{c}p-1\\ k\end{array}}\right) \pmod {p^{2}}, \end{aligned}\) where \(r\in \{ 1,2,3\} \) .
