This study first assesses the performance of regional climate models in the Coordinated Regional Climate Downscaling Experiment (CORDEX) in reproducing observed extreme precipitation indices over the Greater Horn of Africa (GHA) region during 1989-2005. The study then assesses projected changes in these extremes during 2069-2098 compared to 1976-2005. The Regional Climate Model (RCM) simulations are made using two RCMs, with large-scale forcing from four CMIP5 Global limate Models(GCMs) under two Representative Concentration Pathways (RCP4.5 and RCP8.5). We found that RCM simulations have reasonably captured observed patterns of moderate precipitation extreme indices (MPEI). Pattern correlation coefficients between simulated and observed MPEI exceed 0.5 for all except the Simple Daily Intensity Index (SDII). However, significant overestimations or underestimations exist over localized areas in the region. Projected changes in Total annual Precipitation (PRCPTOT) and the annual number of heavy (>10 mm) and very heavy (>20 mm) precipitation days by 2069-2098 show a general north-south pattern, with decreases over the southern half and increases over the northern half of the GHA. These changes are often greatest over parts of Somalia, Eritrea, the Ethiopian highlands and southern Tanzania. Maximum one-and five-day precipitation totals over a year and SDII (ratio of PRCPTOT to rainy days) are projected to increase over a majority of the GHA, including areas where PRCPTOT is projected to decrease, suggesting fewer, but heavier rainy days in the future. Changes in the annual sum of daily precipitation above the 95th and 99th percentiles are statistically significant over a few locations, with the largest projected decrease/increase over Eritrea and northwestern Sudan/Somalia. Projected changes in Consecutive Dry Days (CDD) suggest longer periods of dryness over the majority of the GHA, except the central portions covering northern Uganda, southern South Sudan, southeastern Ethiopia and Somalia. Substantial increases in CDD are located over southern Tanzania and the Ethiopian highlands. The magnitude and the spatial extent of statistically-significant changes in all MPEI increase from RCP4.5 to RCP8.5, and the separation between positive and negative changes becomes clearer under RCP8.5.