Network embedding has been proven to be helpful for many real-world problems. In this paper, we present a scalable multiplex network embedding model to represent information of multi-type relations into a unified embedding space. To combine information of different types of relations while maintaining their distinctive properties, for each node, we propose one high-dimensional common embedding and a lower-dimensional additional embedding for each type of relation. Then multiple relations can be learned jointly based on a unified network embedding model. We conduct experiments on two tasks: link prediction and node classification using six different multiplex networks. On both tasks, our model achieved better or comparable performance compared to current state-of-the-art models with less memory use.