Modern Log-Structured Merge-tree (LSM-tree) based Key-Value (KV) stores built on SSDs become a crucial storage paradigm for enabling a variety of applications. In an LSM-tree, in-memory writes are first stored in a sorted buffer and periodically flushed to disk as Level-0 SSTables. Compaction merges overlapping SSTables to remove redundant entries and enforce global ordering, ensuring that levels above Level-0 remain sorted and non-overlapping. However, the read performance of LSM-tree based KV stores deteriorates on fast SSDs due to severe write interference: (1) the flush operation during write process prolongs the read path; (2) the compaction operation triggered by writes invalidates the read cache. To solve these problems, this paper proposes CalmKV, an interference-resistant KV store on fast SSDs that delivers high read performance. CalmKV improves upon conventional KV stores by incorporating two core components: the L0 Filter Map component to shorten the read path and the Dual-Index Mixed Cache component to improve the cache hit rate. Experimental results show that CalmKV improves read performance by 1.21 \(\times \) to 2.92 \(\times \) compared to state-of-the-art production KV store systems across various workloads.