The evolving worldly dynamics necessitate continuous revision and updating of knowledge within Large Language Models (LLMs), driving the development of Knowledge Editing (KE) techniques. Recently, a novel paradigm of Temporal Knowledge Editing (TKE) has been proposed, emphasizing that models deployed in dynamic environments should integrate new information while retaining historical knowledge. However, we observe that current definitions and methods for TKE are insufficient, as they do not effectively capture or adapt to the fine-grained temporal dynamics inherent in real-world knowledge evolution. In this paper, we introduce the notion of multi-granularity TKE, encompassing temporal knowledge across yearly, monthly, and daily granularities, and propose a corresponding dataset, named MTKE. We argue that comprehending and retaining knowledge across different temporal granularities is crucial for LLMs to accurately reflect real-world changes. The key challenge lies in integrating new temporal knowledge at various granularities while also preserving relevant historical knowledge, thus ensuring LLMs maintain a consistent and accurate understanding over time. To achieve this, we propose a Sparse Parameter-Injected Knowledge Editing method, dubbed SPIKE, which anchors both temporal knowledge and subject positions within the model. Experiments demonstrate that our method effectively preserves historical knowledge performance while accurately incorporating dynamic temporal knowledge across multi-granularity temporal scenarios.