Learning from a sequence of tasks for a lifetime is essential for an agent towards artificial general intelligence. This requires the agent to continuously learn and memorize new knowledge without interference. This paper first demonstrates a fundamental issue of lifelong learning using neural networks, named anterograde forgetting, i.e., preserving and transferring memory may inhibit the learning of new knowledge. This is attributed to the fact that the learning capacity of a neural network will be reduced as it keeps memorizing historical knowledge, and the fact that the conceptual confusion may occur as it transfers irrelevant old knowledge to the current task. This work proposes a general framework named Cycled Memory Networks (CMN) to address the anterograde forgetting in neural networks for lifelong learning. The CMN consists of two individual memory networks to store shortterm and long-term memories to avoid capacity shrinkage. A transfer cell is designed to connect these two memory networks, enabling knowledge transfer from the long-term memory network to the short-term memory network to mitigate the conceptual confusion, and a memory consolidation mechanism is developed to integrate short-term knowledge into the long-term memory network for knowledge accumulation. Experimental results demonstrate that the CMN can effectively address the anterograde forgetting on several task-related, task-conflict, class-incremental and crossdomain benchmarks.