Compute Express Link (CXL), as an emerging high-speed interconnect protocol, offers a promising approach to memory expansion. Organizing fast DDR DRAM and large CXL memory as a tiered memory system is preferred to obtain the large memory capacity while maintaining high memory performance. Additionally, such a tiered memory system also adopts huge pages to alleviate address translation overhead. However, due to memory bloating issues in huge pages, existing hardware-based tiered memory management systems suffer from severe cache conflicts and DDR DRAM underutilization, resulting in significant performance degradation. We introduce Ginkgo, a learned-index enhanced tiered memory system, which builds a distribution-aware cache index mechanism while leveraging the learned index to minimize metadata overhead. Evaluation reveals that Ginkgo reduces average memory access latency with an average of 3.1% and 13.5% compared to state-of-the-art Alloy Cache and Unison Cache, respectively.