To address the issue of catastrophic forgetting in neural networks, we propose a novel, simple, and effective solution called neuron-level plasticity control (NPC). While learning a new task, the proposed method preserves the knowledge for the previous tasks by controlling the plasticity of the network at the neuron level. NPC estimates the importance value of each neuron and consolidates important \textit{neurons} by applying lower learning rates, rather than restricting individual connection weights to stay close to certain values. The experimental results on the incremental MNIST (iMNIST) and incremental CIFAR100 (iCIFAR100) datasets show that neuron-level consolidation is substantially more effective compared to the connection-level consolidation approaches.