The shared e-scooter is a popular and user-convenient mode of transportation, owing to the free-floating manner of its service. The free-floating service has the advantage of offering pick-up and drop-off anywhere, but has the disadvantage of being unavailable at the desired time and place because it is spread across the service area. To improve the level of service, relocation strategies for shared e-scooters are needed, and it is important to predict the demand for their use within a given area. Therefore, this study aimed to develop a demand prediction model for the use of shared e-scooters. The temporal scope was selected as October 2020, when the demand for e-scooter use was the highest in 2020, and the spatial scope was selected as Seocho and Gangnam, where shared e-scooter services were first introduced and most frequently used in Seoul, Korea. The spatial unit for the analysis was set as a 200 m square grid, and the hourly demand for each grid was aggregated based on e-scooter trip data. Prior to predicting the demand, the spatial area was clustered into five communities using the community structure method. The demand prediction model was developed based on long short-term memory (LSTM) and the prediction results according to the activation function were compared. As a result, the model employing the exponential linear unit (ELU) and the hyperbolic tangent (tanh) as the activation function produced good predictions regarding peak time demands and off-peak demands, respectively. This study presents a methodology for the efficient analysis of the wider spatial area of e-scooters.