Abstract: In-network processing methods are often adopted in wireless sensor network (WSN) to reduce data communication and prolong the lifetime of network, which enables a WSN application to be described as a set of tasks (sensing, processing) and dependencies among them. Task assignment has become an important problem which needs to be resolved, as different task assignments can cause different communication traffics, and then cause different energy consumption when performing the application. Based on the task graph of WSN described by DAG (directed acyclic graph), an energy-efficient task assignment framework is proposed. As an application can be decomposed into sensing tasks and processing tasks, the task assignment is presented as a process of sensing task assignment and processing task assignment. Sensing task assignment involves sensor selection in WSN and some work has been done for this problem. In this paper, the authors consider the problem of how to assign the processing tasks after the selection of sensors to make the application performed using minimum energy. The processing task assignment is formulated as a quadratic 0-1 programming problem, and a distributed OALL algorithm (optimizing assignment layer by layer) is proposed. With demonstrative example, the proposed algorithm has been evaluated, and the results of experiment has proved its effectiveness.