Click-through rate (CTR) prediction aims to predict the probability that the user will click an item, which has been one of the key tasks in online recommender and advertising systems. In such systems, rich user behavior (viz. long- and short-term) has been proved to be of great value in capturing user interests. Both industry and academy have paid much attention to this topic and propose different approaches to modeling with long-term and short-term user behavior data. But there are still some unresolved issues. More specially, (1) rule and truncation based methods to extract information from long-term behavior are easy to cause information loss, and (2) single feedback behavior regardless of scenario to extract information from short-term behavior lead to information confusion and noise. To fill this gap, we propose a Graph based Long-term and Short-term interest Model, termed GLSM. It consists of a multi-interest graph structure for capturing long-term user behavior, a multi-scenario heterogeneous sequence model for modeling short-term information, then an adaptive fusion mechanism to fused information from long-term and short-term behaviors. Comprehensive experiments on real-world datasets, GLSM achieved SOTA score on offline metrics. At the same time, the GLSM algorithm has been deployed in our industrial application, bringing 4.9% CTR and 4.3% GMV lift, which is significant to the business.