We propose in this paper a combined model of Long Short Term Memory and Convolutional Neural Networks (LSTM-CNN) that exploits word embeddings and positional embeddings for cross-sentence n-ary relation extraction. The proposed model brings together the properties of both LSTMs and CNNs, to simultaneously exploit long-range sequential information and capture most informative features, essential for cross-sentence n-ary relation extraction. The LSTM-CNN model is evaluated on standard dataset on cross-sentence n-ary relation extraction, where it significantly outperforms baselines such as CNNs, LSTMs and also a combined CNN-LSTM model. The paper also shows that the LSTM-CNN model outperforms the current state-of-the-art methods on cross-sentence n-ary relation extraction.