Offline signature verification is a challenging issue that is widely used in various fields. Previous approaches model this task as a static feature matching or distance metric problem of two images. In this paper, we propose a novel Static-Dynamic Interaction Network (SDINet) model which introduces sequential representation into static signature images. A static signature image is converted to sequences by assuming pseudo dynamic processes in the static image. A static representation extracting deep features from signature images describes the global information of signatures. A dynamic representation extracting sequential features with LSTM networks characterizes the local information of signatures. A dynamic-to-static attention is learned from the sequences to refine the static features. Through the static-to-dynamic conversion and the dynamic-to-static attention, the static representation and dynamic representation are unified into a compact framework. The proposed method was evaluated on four popular datasets of different languages. The extensive experimental results manifest the strength of our model.