In this paper we establish some new congruences involving Catalan numbers as well as central binomial coefficients. Let p>3 be a prime. We show that sum_{k=0}^{p-1}C_{pn+k}/C_n=1-3(n+1)((p-1)/3) (mod p^2) for every n=0,1,2,..., where C_m is the Catalan number binom(2m,m)/(m+1), and (*/3) is the Legendre symbol. We also determine sum_{k=0}^{p^a-1}binom(2k,k+d) and sum_{k=0}^{p^a-1}k*binom(2k,k+d) modulo p^2 for all a=1,2,3,... and d=0,1,...,p.