Cross-sentence n-ary relation extraction detects relations among n entities across multiple sentences. Typical methods formulate an input as a document graph, integrating various intra-sentential and inter-sentential dependencies. The current state-of-the-art method splits the input graph into two DAGs, adopting a DAG-structured LSTM for each. Though being able to model rich linguistic knowledge by leveraging graph edges, important information can be lost in the splitting procedure. We propose a graph-state LSTM model, which uses a parallel state to model each word, recurrently enriching state values via message passing. Compared with DAG LSTMs, our graph LSTM keeps the original graph structure, and speeds up computation by allowing more parallelization. On a standard benchmark, our model shows the best result in the literature.