A Hashgraph-based data management method for building Internet of Things （IoT） was proposed to address the problems of severe lack of throughput and high response delay when applying blockchain to the building IoT scenarios. In this method， Directed Acyclic Graph （DAG） was used for data storage to increase the throughput performance of blockchain because of the high concurrency of schematic structure； Hashgraph algorithm was applied to reach consensus on the data stored in DAG to reduce the time consumption of consensus； the smart contracts were designed to realize access control to prevent unauthorized users from operating data. Caliper， a blockchain performance testing tool， was adopted for performance test. The results show that in a medium-scale simulation environment with 32 nodes， the throughput of the proposed method is 1 063.1 transactions per second， which is 6 times and 3 times than that of the edge computing and the cross-chain methods； the data storage delay and control delay of the proposed method are 4.57 seconds and 4.92 seconds respectively， indicating that the proposed method has the response speed better than the comparison methods； and the transaction success rate of this method reaches 87.4% in spike testing. At the same time， the prototype system based on this method can run stably for 120 hours in stability testing. The above illustrates that the proposed method can effectively improve the throughput and response speed of blockchain， and meets actual needs in the building IoT scenarios.