Existing dialog systems are all monolingual, where features shared among different languages are rarely explored. In this paper, we introduce a novel multilingual dialogue system. Specifically, we augment the sequence to sequence framework with improved shared-private memory. The shared memory learns common features among different languages and facilitates a cross-lingual transfer to boost dialogue systems, while the private memory is owned by each separate language to capture its unique feature. Experiments conducted on Chinese and English conversation corpora of different scales show that our proposed architecture outperforms the individually learned model with the help of the other language, where the improvement is particularly distinct when the training data is limited.