In this paper, we consider asynchronous update scheme for a variant of graph rewriting systems called graph-rewriting automata, and show that synchronous update can be simulated by asynchronous update using a constructed rule set from the one for synchronous update. It is well known that such rule construction is possible on cellular automata or other automata networks whose structures are fixed, but graph rewriting automata induce structural changes and additional mechanism of communication and local synchronization is required. Some simple examples are given by simulation.