Influence maximization is currently a most extensively researched topic in social network analysis. Existing approaches tackle this task by either pursuing the real influence strength of a node or designing proper measurements for estimating it. The degree is a popularly adopted influence strength metric, based on which a variety of methods have been developed. Though with good efficiency, degree-based methods suffer unsatisfactory accuracy since this metric only covers a limited considered scale over the whole network of interest and also lacks discriminatory power. In this paper, we propose a novel influence maximization method, named Fixed Neighbour Scale (FNS), which extracts useful information from multiple levels of neighbours for a target node to estimate its influence strength, rather than only considering directly connected neighbours as in degree-based methods. To facilitate the implementation of FNS, we also present a centrality measurement termed FNS-dist, which estimates a node’s influence strength by summing its multi-level neighbours’ weights that are mainly determined by their distances to the target node. Experiments conducted on nine networks of different sizes and categories show that the proposed FNS method achieves excellent and stable performance compared with other algorithms based on designing metrics for measuring influence strength. We also exhibit that FNS-dist is a superior alternative centrality which is more proper and precise than the degree.