In the Blockchain system, sharding is the main on-chain expansion solution, and state sharding can solve the scalability problem of the public chain without reducing security. However, the introduction of sharding technology has also brought in the processing problem of cross-shard transaction verification. When most transactions in the system are cross-shard transactions, the ability of processing cross-shard transactions determines the performance of the entire system. Therefore, cross-sharding transaction verification and processing strategies are very important in the process of designing the sharding system. In response to the above problems, this study proposes a state reduction and multi-round (SRMR) scheme that uses state reduction combined with multiple rounds of verification within shards to process cross-shard transactions. First, the probability of cross-shard transactions is analyzed, and then the probability of cross-shard transaction processing in each layer is evaluated under the proposed model of using state reduction to process cross-shard transactions. It is found that the state reduction model alone will make the upper-layer shard transaction load unduly large. Thus, the incentive mechanism and the state reduction combined with multi-round verification are put forward to balance the upper-layer transaction load. Finally, the value of reasonable rounds is obtained, and a strategy of reasonably balancing reduction and multi-round verification is presented. This scheme comprehensively utilizes the capabilities of nodes to ensure the smooth completion of cross-shard transactions and reduce the rollback per cross-shard transaction.