We present an effective and efficient approach for low-light image enhancement, named Lookup Table Global Curve Estimation (LUT-GCE). In contrast to existing curve-based methods with pixel-wise adjustment, we propose to estimate a global curve for the entire image that allows corrections for both under- and over-exposure. Specifically, we develop a novel cubic curve formulation for light enhancement, which enables an image-adaptive and pixel-independent curve for the range adjustment of an image. We then propose a global curve estimation network (GCENet), a very light network with only 25.4k parameters. To further speed up the inference speed, a lookup table method is employed for fast retrieval. In addition, a novel histogram smoothness loss is designed to enable zero-shot learning, which is able to improve the contrast of the image and recover clearer details. Quantitative and qualitative results demonstrate the effectiveness of the proposed approach. Furthermore, our approach outperforms the state of the art in terms of inference speed, especially on high-definition images (e.g., 1080p and 4k).