In this paper, we establish some congruences mod $p^3$ involving the sums $\sum _{k=1}^{p-1}{k}^m{B}_{p,k}^{2l}$, where $p>3$ is a prime number and $B_{p,k}$ are generalized Catalan numbers. We also establish some congruences mod $p^2$ involving the sums $\sum _{k=1}^{p-1}{k}^m{B}_{p,k}^{2l_1}{B}_{p,k-d}^{2l_2}$, where $m,l_1,l_2,d$ are positive integers and $1\le d\le p-1$.