A modified opinion dynamic model is proposed which concerned two factors: similarity and randomness of network structure. The former mainly considered the common friends of individuals, and the latter considered the randomness of connections between individuals. The results of the model indicate that the node degree has a great influence on the formation of individuals’ opinions. The larger node degree, the possibility of individuals’ opinions come to consensus is higher. Under the same node degree, individuals’ opinions are more likely to form consensus in regular network than in random network. But the less time required for individuals’ opinions come to stable with the increase of randomness of network structure, which indicates that the randomness can speed up the spread of opinions. The results also represent that the small-world network that with small random links is the best place that individuals are incline to consensus when node degree is greater than 6. Our work provides some insights to the understanding of the role of similarity of network structure and the node degree in the formation of individuals’ opinions.