Remembering and forgetting mechanisms are two sides of the same coin in a human learning-memory system. Inspired by human brain memory mechanisms, modern machine learning systems have been working to endow machine with lifelong learning capability through better remembering while pushing the forgetting as the antagonist to overcome. Nevertheless, this idea might only see the half picture. Up until very recently, increasing researchers argue that a brain is born to forget, i.e., forgetting is a natural and active process for abstract, rich, and flexible representations. This paper presents a learning model by active forgetting mechanism with artificial neural networks. The active forgetting mechanism (AFM) is introduced to a neural network via a "plug-and-play" forgetting layer (P\&PF), consisting of groups of inhibitory neurons with Internal Regulation Strategy (IRS) to adjust the extinction rate of themselves via lateral inhibition mechanism and External Regulation Strategy (ERS) to adjust the extinction rate of excitatory neurons via inhibition mechanism. Experimental studies have shown that the P\&PF offers surprising benefits: self-adaptive structure, strong generalization, long-term learning and memory, and robustness to data and parameter perturbation. This work sheds light on the importance of forgetting in the learning process and offers new perspectives to understand the underlying mechanisms of neural networks.