With the rapid proliferation of integration of blockchain and IoT, traditional centralized architectures and single-node processing have been effectively solved, but scalability of blockchain have become inadequate to meet the demands of high-load environments. Sharded blockchain brings an innovative approach to tackle the scalability of blockchain and has the potential to greatly enhance the performance of IoT based on blockchain. This paper introduces CTS towards IoT – complete tree sharding that overlaps shards to enable a little shards to retain records of other shards, facilitating the validation of cross-shard transactions as intra-shard transactions. A tree sharding consensus mechanism that relies on the complete tree architecture is proposed to ensure consistency among interconnected shards during the execution of cross-shard transactions. A prototype for CTS towards IoT is simulated and the findings demonstrate that CTS can enhance transaction throughput by a factor of 1.3 when compared to state of the art layered sharding systems observed in a system consisting of 15 shards and 1500 nodes.