For a more compatible and consistent high dynamic range (HDR) viewing experience, a new image format with a double-layer structure has been developed recently, which incorporates an auxiliary Gain Map (GM) within a standard dynamic range (SDR) image for adaptive HDR display. This new format motivates us to introduce a new task termed Gain Map-based Inverse Tone Mapping (GM-ITM), which focuses on learning the corresponding GM of an SDR image instead of directly estimating its HDR counterpart, thereby enabling a more effective up-conversion by leveraging the advantages of GM. The main challenge in this task, however, is to accurately estimate regional intensity variation with the fluctuating peak value. To this end, we propose a dual-branch network named GMNet, consisting of a Local Contrast Restoration (LCR) branch and a Global Luminance Estimation (GLE) branch to capture pixel-wise and image-wise information for GM estimation. Moreover, to facilitate the future research of the GM-ITM task, we build both synthetic and real-world datasets for comprehensive evaluations: synthetic SDR-GM pairs are generated from existing HDR resources, and real-world SDR-GM pairs are captured by mobile devices. Extensive experiments on these datasets demonstrate the superiority of our proposed GMNet over existing HDR-related methods both quantitatively and qualitatively. The codes and datasets are available at https://github.com/qtlark/GMNet.