Landform mapping is the initial step of many geomorphological analyses (e.g. assessment of natural hazards and natural resources) and requires vast resources to be applied to wide areas at high-resolution. Among geomorphological objects, we focus on glacial moraine mapping, since it is a task relevant to many fields (e.g. paleoclimate and glacial geomorphology). Here we proposed to exploit the potential of Deep Learning-based approaches to map moraine land-forms by exploiting multi-source remote sensing imagery. To this end, we propose the first Deep Learning model to map glacial moraines, namely MorNet. As multi-source remote sensing information, we combine together three different sources: Topographic (Pleiades-derived DSM), Multispectral (Sentinel-2), and SAR (Sentinel-1) data. To cope with such hetero- geneous information, the proposed model has a dedicated branch for each input source and, a late fusion mechanism is leveraged to combine them with the aim to provide the final mapping. The performance of the MorNet model is evaluated on several glacier valleys in China in the Himalayan range. This area contains minimally eroded moraines, so they are well-defined and of varied morphology. The behavior of the proposed method is compared to models using individual mono-source models in order to highlight the benefit to simultaneously leverage multi-source information. The use of multi-source data allows MorNet to exploit the complementarity of the three input sources and improve its performance from an f1-score of about 41.6 using a single source to 52.8 using three sources. MorNet provides a first-order moraine map through its ability to identify well-defined moraines. Consequently, MorNet can identify areas likely to contain moraines and intends to be used as a tool by experts to facilitate and support large-scale mapping.