Lifelong learning is a crucial issue in advanced artificial intelligence. It requires the learning system to learn and accumulate knowledge from sequential tasks. The learning system needs to deal with increasingly more domains and tasks. We consider that the key to an effective and efficient lifelong learning system is the ability to memorize and recall the learned knowledge using neural networks. Following this idea, we propose Generative Memory (GM) as a novel memory module, and the resulting lifelong learning system is referred to as the GM Net (GMNet). To make the GMNet feasible, we propose a novel learning mechanism, referred to as P -invariant learning method. It replaces the memory of the real data by a memory of the data distribution, which makes it possible for the learning system to accurately and continuously accumulate the learned experiences. We demonstrate that GMNet achieves the state-of-the-art performance on lifelong learning tasks.