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• We propose a new complexity measure of time series called discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph. • We use amplitude difference distribution instead of degree distribution to be the distribution probability extracted from horizontal visibility graph. • We validate the method with logistic map and Hénon map, and find it has higher accuracy and sensitivity than the traditional method in characterizing dynamical systems. • Stock markets of different area are distinguished well by our method, and it can get the result that the US market and the Hong Kong market are more developed than the Chinese mainland market, which is consistent with the reality. In this paper, we propose discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph as a new complexity measure of nonlinear time series. We use amplitude difference distribution instead of degree distribution to extract information from the network constructed from the horizontal visibility graph, and combine amplitude difference distribution with discrete generalized past entropy to propose the new method. By analyzing the logistic map and Hénon map with the proposed method, we find the proposed method not only can assess systems well, but also has higher accuracy and sensitivity than the traditional method in characterizing dynamical systems. Furthermore, we apply the proposed method to the financial data: the six indices from Chinese mainland, Hong Kong and US. The result shows that the US market and the Hong Kong market are more developed than the Chinese mainland market, which is consistent with the reality. [ABSTRACT FROM AUTHOR]