Abstract Spreading process is a common phenomenon in complex networks. Identifying important nodes in complex networks is of great significance in real-world applications. Based on the spreading process on networks, a lot of measures have been proposed to evaluate the importance of nodes. However, most of the existing measures are appropriate to static networks, which are fragile to topological perturbations. Many real-world complex networks are dynamic rather than static, meaning that the nodes and edges of such networks may change with time, which challenge numerous existing centrality measures. Based on a new weighted mechanism and the newly proposed H-index and LeaderRank (LR), this paper introduces a variant of the LR measure, called adaptive LeaderRank (ALR), which is a new member of the LR-family. Simulations on six real-world networks reveal that the new measure can well balance between prediction accuracy and robustness. More interestingly, the new measure can better adapt to the adjustment or local perturbations of network topologies, as compared with the existing measures. By discussing the detailed properties of the measures from the LR-family, we illustrate that the ALR has its competitive advantages over the other measures. The proposed algorithm enriches the measures to understand complex networks, and may have potential applications in social networks and biological systems.