Network representations are powerful tools for the analysis of time-varying financial complex systems consisting of multiple co-evolving financial time series, e.g., stock prices, etc. In this work, we develop a new kernel-based similarity measure between dynamic time-varying financial networks. Our ideas is to transform each original financial network into quantum-based entropy time series and compute the similarity measure based on the classical dynamic time warping framework associated with the entropy time series. The proposed method bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks abstracted from financial time series of New York Stock Exchange (NYSE) database demonstrate that our approach can effectively discriminate the abrupt structural changes in terms of the extreme financial events.