The traditional page-grained buffer manager in database systems has a low hit ratio when only a few tuples within a page are frequently accessed. To handle this issue, this paper proposes a new buffering scheme called the AMG-Buffer (Adaptive Multi-Grained Buffer). AMG-Buffer proposes to use two page buffers and a tuple buffer to organize the whole buffer. In this way, the AMG-Buffer can hold more hot tuples than a single page-grained buffer. Further, we notice that the tuple buffer may cause additional read I/Os when writing dirty tuples into disks. Thus, we introduce a new metric named clustering rate to quantify the hot-tuple rate in a page. The use of the tuple buffer is determined by the clustering rate, allowing the AMG-Buffer to adapt to different workloads. We conduct experiments on various workloads to compare the AMG-Buffer with several existing schemes, including LRU, LIRS, CFLRU, CFDC, and MG-Buffer. The results show that AMG-Buffer can significantly improve the hit ratio and reduce I/Os compared to its competitors. Moreover, the AMG-Buffer achieves the best performance on a dynamic workload as well as on a large data set, suggesting its adaptivity and scalability to changing workloads.