The existing evaluation methods for node importance in complex network mainly focus on undirected-unweighted complex networks, and can not reflect objectively the reality of some real world status. Focusing on the problems such as the limited scope of evaluation indexes and not enough comprehensive evaluation results in the undirected-weighted and directed-weighted networks, and the node importance evaluation method in undirected-unweighted networks based on mutual information was used for reference, a new evaluation method based on mutual information that is suitable for the undirected-weighted and directed-weighted networks was proposed. In this method, each edge was regarded as a flow of information, the structure characteristics of the corresponding complex networks and the definition method of "amount of information" were considered, then the amount of information was calculated as the node importance evaluation index. The analyses of the instance network show that the proposed algorithm can more detailed describe the differences between nodes in the directed-weighted network under the premise of guaranteeing estimation accuracy. In the evaluation of the ARPA (Advanced Research Project Agency) network nodes, the first five most important nodes number that were evaluated from the proposed algorithm and the previous indexes were especially close, so the algorithm's ability of finding the core nodes was highlighted. The proposed algorithm provides a certain theoretical help for evaluating the core nodes in the undirected-weighted and directed-weighted networks and improving the network invulnerability ability quickly and accurately.