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Due to the development of microprocessor technology, there are more than 20 billion sensor-based devices connected to the Internet of Things (IoT) to monitor physical phenomena and events. To reduce the energy used by idle listening, a low-duty cycle is often used in an event-sparse wireless sensor network. However, low-duty cycles bring large end-to-end delays. In this paper, a listen interval adaptive adjustment (LIAA) scheme is proposed to adjust the listen interval (LI) of a node to reduce end-to-end delays while maintaining the long lifetime of a network. The key idea is to make full use of the energy consumption imbalance in a network, to allow nodes away from the sink to use the residual energy to add listen intervals. The LIAA scheme has 3 sub-strategies. One is the basic add listen interval (BALI) strategy, in which the parent node adds listen intervals in the fixed active slots of its child nodes. Another strategy is the consecutive listen (CL) scheme, which is based on BALI, and listen intervals are added consecutively. The third strategy is the random add listen interval (RALI) scheme, which uses the idea of randomness to add listen intervals. The extensive theoretical analysis and experimental results show that the LIAA scheme proposed in this paper has better performance. Compared with the traditional scheme, the delays in the BALI scheme, CL scheme and RALI scheme were reduced by 24.03%, 23.45% and 39.41%, respectively, while the lifetime of the network was maintained. [ABSTRACT FROM AUTHOR]