Session-based recommendation aims to predict a user's next action based on previous actions in the current session. The major challenge is to capture authentic and complete user preferences in the entire session. Recent work utilizes graph structure to represent the entire session and adopts Graph Neural Network to encode session information. This modeling choice has been proved to be effective and achieved remarkable results. However, most of the existing studies only consider each item within the session independently and do not capture session semantics from a high-level perspective. Such limitation often leads to severe information loss and increases the difficulty of capturing long-range dependencies within a session. Intuitively, compared with individual items, a session snippet, i.e., a group of locally consecutive items, is able to provide supplemental user intents which are hardly captured by existing methods. In this work, we propose to learn multi-granularity consecutive user intent unit to improve the recommendation performance. Specifically, we creatively propose Multi-granularity Intent Heterogeneous Session Graph which captures the interactions between different granularity intent units and relieves the burden of long-dependency. Moreover, we propose the Intent Fusion Ranking module to compose the recommendation results from various granularity user intents. Compared with current methods that only leverage intents from individual items, IFR benefits from different granularity user intents to generate more accurate and comprehensive session representation, thus eventually boosting recommendation performance. We conduct extensive experiments on five session-based recommendation datasets and the results demonstrate the effectiveness of our method.