In wireless sensor networks (WSNs), the sensed data of each node are usually gathered through a data collection tree rooted at the sink node. The data collection tree generated randomly usually does not have the longest network lifetime. How to prolong the network lifetime is one of the main challenges in WSNs. In this paper, we propose a switching algorithm with prediction strategy (SAPS) to enhance the lifetime of WSNs through reducing the load of the node with the highest load by switching its descendants. In SAPS, the shortest path to the sink is chosen for each switched node to ensure that the routing tree is shortest, thus reducing the delay and energy expenditure of data collection. Furthermore, a prediction strategy which ensures that the highest load in the network decreases in each switching is developed to guarantee high efficiency and fast convergence of the algorithm. A distributed version of our algorithm, called DSAPS, is also designed. Simulation results demonstrate that our algorithms outperform existing methods in terms of network lifetime, maximum level of the routing tree, energy expenditure of switching, energy expenditure of data collection in each round, and rate of convergence.