Low-light images suffer from severe noise and low illumination. Current deep learning models that are trained with real-world images have excellent noise reduction, but a ratio parameter must be chosen manually to complete the enhancement pipeline. In this work, we propose an adaptive low-light raw image enhancement network to avoid parameter-handcrafting and to improve image quality. The proposed method can be divided into two sub-models: Brightness Prediction (BP) and Exposure Shifting (ES). The former is designed to control the brightness of the resulting image by estimating a guideline exposure time $t_1$. The latter learns to approximate an exposure-shifting operator $ES$, converting a low-light image with real exposure time $t_0$ to a noise-free image with guideline exposure time $t_1$. Additionally, structural similarity (SSIM) loss and Image Enhancement Vector (IEV) are introduced to promote image quality, and a new Campus Image Dataset (CID) is proposed to overcome the limitations of the existing datasets and to supervise the training of the proposed model. Using the proposed model, we can achieve high-quality low-light image enhancement from a single raw image. In quantitative tests, it is shown that the proposed method has the lowest Noise Level Estimation (NLE) score compared with the state-of-the-art low-light algorithms, suggesting a superior denoising performance. Furthermore, those tests illustrate that the proposed method is able to adaptively control the global image brightness according to the content of the image scene. Lastly, the potential application in video processing is briefly discussed.