Clustering sensor nodes is an effective method for routing in Wireless Sensor Networks (WSNs), which maximizes the network lifetime and reduces the energy consumption. However, in a clustered-WSN, the Cluster Heads (CHs) bear a higher load compared to the other nodes, which leads to their earlier death. Therefore, minimizing the maximum load of the CHs is an important problem, which is called the Load-Balanced Clustering Problem (LBCP). LBCP is an NP-hard problem and the best-known approximation factor for this problem is 1.5. Moreover, it has been shown that there is no polynomial-time approximation algorithm that solves this problem with a better approximation factor. In this paper, we propose a Fixed Parameter Tractable (FPT) approximation algorithm with an approximation factor of 1.2 for LBCP. We also propose an energy-efficient and energy-balanced routing algorithm for routing between the CHs and the sink. The simulation results show that the proposed algorithm is practical for large-scale WSNs and performs better than the other similar algorithms.