Over the past few decades, Uganda has suffered from many damaging landslides like the 2010 Bududa, 1994 Kisomoro and 1966 Rwenzori events. Although most slope failures are rainfall-induced, earthquakes can also trigger larger scale landslides. Despite escalating landslide risk exacerbated by rapid population growth and urbanization coupled with a substandard building stock, comprehensive national co-seismic and rainfall-induced landslide hazard and risk maps for Uganda do not exist. This study aims to develop a co-seismic landslide hazard susceptibility framework using a geospatial-based fuzzy logic methodology. Initially landslide conditioning factor maps are created, aggregated with a stochastic event-based probabilistic seismic hazard model developed using OpenQuake-engine, and their spatial distribution is overlaid to produce final fuzzy sets describing relative probabilities of co-seismic landslide hazard. Seismic hazard map for a 475-year return period shows maximum bedrock peak ground acceleration increasing to 0.27 g in western Uganda. Further results show that areas of Precambrian granites located in upper slopes with gradients between 35 and 40o have the highest landslide frequency ratios. Whilst the majority of the country is exposed to relatively low hazard, the Rwenzori and Kigezi regions are highly susceptible to co-seismic landslides. To reduce the earthquake and landslide risks across Uganda, it is recommended that the directorate of disaster preparedness and management should develop suitable disaster risk mitigation measures like: local planning and zoning, structural retrofitting and infrastructure protection for key public buildings, natural system protection, and education towards raising community awareness.