Linear prediction is a popular strategy employed in the analysis and representation of signals. In this paper, we propose a new linear prediction approach by considering the standard linear prediction in the context of graph signal processing, which has gained significant attention recently. We view the signal to be defined on the nodes of a graph with an adjacency matrix constructed using the coefficients of the standard linear predictor (SLP). We prove theoretically that the graph based linear prediction approach results in an equal or better performance compared with the SLP in terms of the prediction gain. We illustrate the proposed concepts by application to real speech signals.