Automatic evaluating the performance of Open-domain dialogue system is a challenging problem. Recent work in neural network-based metrics has shown promising opportunities for automatic dialogue evaluation. However, existing methods mainly focus on monolingual evaluation, in which the trained metric is not flexible enough to transfer across different languages. To address this issue, we propose an adversarial multi-task neural metric (ADVMT) for multi-lingual dialogue evaluation, with shared feature extraction across languages. We evaluate the proposed model in two different languages. Experiments show that the adversarial multi-task neural metric achieves a high correlation with human annotation, which yields better performance than monolingual ones and various existing metrics.