In this paper, we propose a new rate-based congestion control method for Named Data Networking (NDN) using additive increase multiplicative decrease (AIMD) and explicit rate notification. In the proposed method, routers notify a corresponding consumer of bottleneck bandwidth by use of Data packets, in a relatively long interval. In addition, routers monitor outgoing faces using the leaky bucket mechanism. When congestion is detected, the routers report this to corresponding consumers using negative-acknowledgment (NACK) packets. A consumer sets its Interest sending rate to the reported rate when a new value is reported. In addition, the consumer adjusts the sending rate to be around the reported rate based on the AIMD mechanism at Data/NACK packet reception. Computer simulations show that the proposed method achieves a high throughput performance and max-min fairness thanks to the effective congestion avoidance.