This paper proposes a novel power index considering the dual influence of voting rules and social network effect. We analyzed the influence of the change of voter's viewpoint on voting result based on the influence network which is designed by constructing the social network of decision group and measuring the degree of influence between nodes. The ability of voters to achieve their own decision purpose by influencing others' behavior is defined as the network power, and a network power measure method is proposed by extending the power index of Banzhaf. The properties and influencing factors of the network power index, and its difference from Banzhaf power and network centrality are analyzed. Results show that the individual at the center of the social network may become the key voter because of having more power outside the ‘rule power’, and a voter with higher ‘rule power’ may become a weak power person because of being on the edge of a group. The proposed power takes into account the direct and indirect effects of voters, which provides a method to accurately identify key voters.