In this paper, we present a novel image enhancement network consisting of global and local color enhancement. The proposed network model is constructed using global transformation functions, which are formed by a set of piece-wise quadratic curves and a local color enhancement network based on the encoder–decoder network. To adaptively and dynamically control the ranges of each piece-wise curve, we introduce deformable control points (DCPs), which determine the overall structure of the global transformation functions. The parameters for piece-wise quadratic curve fitting and DCPs are estimated using the proposed DCP network (DCPNet). DCPNet processes a down-sampled image to derive the DCP parameters: The DCP offsets and the curve parameters. Then, we obtain a set of DCPs from the DCP offsets and connect each adjacent DCP pair by using the curve parameter to construct a global transformation function for each color channel. The original input images are then transformed based on the resulting transformation functions to obtain globally enhanced images. Finally, the intermediate image is fed into the local enhancement network, which has a U-Net architecture, to produce the spatially enhanced images. Extensive experimental results demonstrate the superiority of the proposed method over state-of-the-art methods in various image enhancement tasks, such as image retouching, tone-mapping, and underwater image enhancement.