In this paper, we mainly establish some congruences involving binomial coefficients and Apéry-like numbers, for example, we prove the following result which was conjectured by Z.-H. Sun: Let p > 3 be a prime. Then \(\sum_{k=0}^{p-1}\left(\begin{array}{c}2k\\ k\end{array}\right)\frac{W_k}{(-12)^k}\equiv\begin{cases}L^2-2p\;({\rm{mod}}\;p^2) & {\rm{if}}\;p\equiv1\;({\rm{mod}}\;3)\;\& \;4p=L^2+27M^2,\\0\;({\rm{mod}}\;p^2) & {\rm{if}}\;p\equiv2\;({\rm{mod}}\;3),\end{cases}\) where L, M are integers and \(W_n=\sum\begin{array}{c}\lfloor\frac{n}{3}\rfloor\\k=0\end{array}\left(\begin{array}{c}2k\\ k\end{array}\right)\left(\begin{array}{c}3k\\k\end{array}\right)\left(\begin{array}{c}n\\ 3k\end{array}\right)(-3)^{n-3k}\) are the second kind Apéry-like numbers.
