Aviation is responsible for approximately 5% of global warming and is expected to increase substantially in the future. Given the continuing expansion of air traffic, mitigation of aviation’s climate impact becomes challenging but imperative. Among various mitigation options, hybrid-electric aircraft (HEA) have drawn intensive attention due to their considerable potential in reducing greenhouse gas emissions (e.g., CO2). However, the non-CO2 effects (especially contrails) of HEA on climate change are more challenging to assess. As the first step to understanding the climate impact of HEA, this research investigates the effects on the formation of persistent contrails when flying with HEA. The simulation is performed using an Earth System Model (EMAC) coupled with a submodel (CONTRAIL), where the contrail formation criterion, the Schmidt–Appleman criterion (SAC), is adapted to globally estimate changes in the potential contrail coverage (PCC). We compared the HEA to conventional (reference) aircraft with the same characteristics, except for the propulsion system. The analysis showed that the temperature threshold of contrail formation for HEA is lower; therefore, conventional reference aircraft can form contrails at lower flight altitudes, whereas the HEA does not. For a given flight altitude, with a small fraction of electric power in use (less than 30%), the potential contrail coverage remained nearly unchanged. As the electric power fraction increased, the reduction in contrail formation was mainly observed in the mid-latitudes (30° N and 40° S) or tropical regions and was very much localized with a maximum value of about 40% locally. The analysis of seasonal effects showed that in non-summer, the reduction in contrail formation using electric power was more pronounced at lower flight altitudes, whereas in summer the changes in PCC were nearly constant with respect to altitude.