Prolonging the network lifetime is one of the fundamental requirements in wireless sensor networks (WSNs). Sensor node clustering is a very popular energy conservation strategy in WSNs, allowing to achieve energy efficiency, low latency, and scalability. According to this strategy, sensor nodes are grouped into several clusters, and one sensor node in each cluster is assigned to be a cluster head (CH). The responsibility of each CH is to aggregate data from the other sensor nodes within its cluster and send these data to the sink. However, the distribution of sensor nodes in the sensing region is often non-uniform, which may lead to an unbalanced number of sensor nodes between clusters and thus unbalanced energy consumption between CHs. This, in turn, may result in a reduced network lifetime. Furthermore, a different number of clusters lead to a different quality of service of a WSN system. To address the problems of unbalanced number of sensor nodes between clusters and selecting an optimal number of clusters, this study proposes an energy-balanced cluster-routing protocol (EBCRP) based on particle swarm optimization (PSO) with five mutation operators for WSNs. The five mutation operators are specially proposed to improve the performance of PSO in optimizing sensor node clustering. A rotation CH selection scheme based on the highest residual energy is used to dynamically select a CH for each cluster in each round. Simulation results show that the proposed EBCRP method performs well in balancing energy consumption and prolonging the network lifetime.