The degradation and attenuation of light in underwater images impose constraints on underwater vision tasks. However, the complexity and the low real-time performance of most current image enhancement algorithms make them challenging in practical applications. To address the above issues, we propose a new lightweight framework for underwater image enhancement. We adopt the curve estimation to learn the mapping between images rather than end-to-end networks, which greatly reduces the requirement for computing resources. Firstly, a designed iterative curve with parameters is used to simulate the mapping from the raw to the enhanced image. Then, the parameters of this curve are learned with a parameter estimation network called CieNet and a set of loss functions. Experimental results demonstrate that our proposed method is superior to existing algorithms in terms of evaluating indexes and visual perception quality. Furthermore, our highly lightweight network enables it to be easily integrated into small devices, making it highly applicable. The extremely short running-time of our method facilitates real-time underwater image enhancement.