Reducing bit-widths of activations and weights of deep networks makes it efficient to compute and store them in memory, which is crucial in their deployments to resource-limited devices, such as mobile phones. However, decreasing bit-widths with quantization generally yields drastically degraded accuracy. To tackle this problem, we propose to learn to quantize activations and weights via a trainable quantizer that transforms and discretizes them. Specifically, we parameterize the quantization intervals and obtain their optimal values by directly minimizing the task loss of the network. This quantization-interval-learning (QIL) allows the quantized networks to maintain the accuracy of the full-precision (32-bit) networks with bit-width as low as 4-bit and minimize the accuracy degeneration with further bit-width reduction (i.e., 3 and 2-bit). Moreover, our quantizer can be trained on a heterogeneous dataset, and thus can be used to quantize pretrained networks without access to their training data. We demonstrate the effectiveness of our trainable quantizer on ImageNet dataset with various network architectures such as ResNet-18, -34 and AlexNet, on which it outperforms existing methods to achieve the state-of-the-art accuracy.