© 2022 IEEE.Stationarity is a well-studied concept in signal processing and the concept of stationary random processes has been extended to graph domains in several recent works. Meanwhile, in many scenarios a globally stationary process model may fail to accurately represent the correlation patterns of the data on the whole graph, e.g. when data is acquired on big graphs or when the behavior of the process varies significantly throughout the graph. In this work, we first propose a locally stationary graph process model, where the overall graph process is expressed through a combination of several local models. We then propose an algorithm that learns a locally stationary graph process model from partially observed realizations of the process. Experimental results show that the proposed locally stationary process model can provide significant gain in signal estimation performance compared to globally stationary models, even in cases where the process is highly stationary.