Face age transformation, which aims to generate a face image in the past or future, has receiving increasing attention due to its significant application value in some special fields, such as looking for a lost child, tracking criminals and entertainment, etc. Currently, most existing methods mainly focus on unidirectional short-span face aging. In this paper, we propose a novel local-global interaction framework for long-span face age transformation. Firstly, we divide a face image into five independent parts and design a local generative network for each of them to learn the local structure changes of a face image, while we utilize a global generative network to learn the global structure changes. Then we introduce an interactive network and an age classification network, which are respectively used to integrate the local and global features and maintain the corresponding age features in different age groups. Given any face image at a certain age, our network can produce a clear and realistic image of face aging or rejuvenation. We test and evaluate the model on complex datasets, and extensive qualitative comparison experiments has proved the effectiveness and immense potential of our proposed method.