The society structure plays an important role in shaping the attitudes, beliefs and public opinion. For studying the role of the society structure in opinion dynamics, we analyze the Sznajd model on small-world network formed by adding shortcuts in a lattice consisting of N nodes arranged in a ring and on two-dimensional (2-D) regular lattice. Through computer simulation, we find that there exists a pseudo-phase transition from the coexistence state for φ<φ_c to the consensus state for φ>φ_c, where φ_c is some threshold for the shortcut density φ, which is dependent of the complex network topology and the dimensionality of complex networks. Our observations indicate the dependence of the opinion dynamics on the complex system topology.