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In order to investigate the evaluation of neuronal firing time series with time, this paper proposed an improved visibility graph method called local visibility graph method for constructing complex networks from time series, which could map time-domain of neuronal firing time series into network domain. By constructing a complex network topology and calculating its statistical properties in a sliding time window, the method described the time-varying statistical characteristics of neuronal firing time series. As a paradigm, three time series of different bursting modes generated by map neuronal model were used to construct networks, realize visualize topology and analyze statistical characteristics. The results show that network topology, average path length and clustering coefficient can depict time-varying morphological characteristics of the time series. The three properties show parameter sensitivity to neuronal bursting. There is a correlation between sparse degree of neuronal bursting and the community size in the complex networks. Evolution characteristics of neuronal firing time series in network-domain can depict their time-domain features, and the ideology proposed in this paper provides a new way for on-line neural signal processing. [ABSTRACT FROM AUTHOR]