Recent years have witnessed the development of visibility graph theory, which allows us to analyze a time series from the perspective of complex network. We in this paper develop a novel time-dependent limited penetrable visibility graph (TDLPVG). Two examples using nonstationary time series from RR intervals and gas liquid flows are provided to demonstrate the effectiveness of our approach. The results of the first example suggest that our TDLPVG method allows characterizing the time-varying behaviors and classifying heart states of healthy, congestive heart failure and atrial fibrillation from RR interval time series. For the second example, we infer TDLPVGs from gas liquid flow signals and interestingly find that the deviation of node degree of TDLPVGs enables to effectively uncover the time-varying dynamical flow behaviors of gas liquid slug and bubble flow patterns. All these results render our TDLPVG method particularly powerful for characterizing the time varying features underlying realistic complex systems from time series. (C) 2017 Elsevier B.V. All rights reserved.