Inundation maps that show water depths that occur in the event of a flood are essential for protection. Especially information on timings is crucial. Creating a dynamic inundation map with depth data in temporal resolution is a major challenge and is not possible with physical models, as these are too slow for real-time predictions. To provide a dynamic inundation map in real-time, we developed a data-driven multi-step inundation forecast system for fluvial flood events. The forecast system is based on a convolutional neural network (CNN), feature-informed dense layers, and a recursive connection from the predicted inundation at timestep t as a new input for timestep t + 1. The forecast system takes a hydrograph as input, cuts it at desired timesteps (t), and outputs the respective inundation for each timestep, concluding in a dynamic inundation map with a temporal resolution (t). The prediction shows a Critical Success Index (CSI) of over 90%, an average Root Mean Square Error (RMSE) of 0.07, 0.12, and 0.15 for the next 6 h, 12 h, and 24 h, respectively, and an individual RMSE value below 0.3 m, for all test datasets when compared with the results from a physically based model.