The theoretical and experimental studies have showed that the topology of the native structure of protein plays an important role in determining its folding process. The complex network approach was used to analyze the topological characters of the native structure of protein and then explore the relationship between these characters and the experimental folding rates. Several types of network were constructed, including all-amino-acids network, hydrophobic amino acid network, hydrophilic amino acid, hydrophobic-hydrophilic amino acid network and their corresponding long-range interaction network. The statistic characters of the assortativity coefficient and the clustering coefficient were studied. The results indicate that all types of network except for the hydrophobic-hydrophilic one are of the positive assortativity coefficient. Furthermore, there is an obvious linear positive correlation between the assortativity coefficient and the folding rate for the all amino acids network and the hydrophobic amino acid network, which implies that the cooperative interactions of the hydrophobic amino acids are important for proteins rapidly folding into their native states. Moreover, it is found that there is a clear linear negative correlation between the clustering coefficient of the hydrophobic amino acid networks and the experimental folding rates of the corresponding proteins, which indicates that the formation of the triangle construction among the amino acids reduces the folding rates. It is also found that in the long-range interaction networks, the formation of contact pairs linking two distant residues in sequence would slow down the process of protein folding.