Catastrophic forgetting is a fundamental challenge in neural networks that prevents continual learning, which is one of the properties essential for achieving true general artificial intelligence. When trained sequentially on multiple tasks, conventional neural networks overwrite previously learned knowledge, hindering their ability to retain and apply past experiences. However, humans and other animals can learn new things continuously without forgetting them. To overcome this problem, we devised an architecture that preserves significant task-specific connections by combining selective neuron freezing with Hebbian learning principles. Hebbian learning enables the network to adaptively strengthen synaptic connections depending on the parameter activation. It is inspired by the synaptic plasticity seen in the brain. By preserving the most important neurons using selective neuron freezing, new tasks can be trained without changing parameter weights. Experiments conducted on standard datasets show that our model significantly reduces the risk of catastrophic forgetting, allowing the network to learn continually.