In this paper the first numerical simulations of condensation trails (contrails) from liquid hydrogen (LH2) fueled aircraft are presented. Such aircraft produces 2.6 times more exhaust water vapor than equivalent aircraft fueled by kerosene; however, combustion of LH2 produces no aerosol particles. LH2 ice crystals, which instead form on background aerosol, are consequently 1--2 orders of magnitude fewer than in a kerosene contrail. LH2 contrails are compared to kerosene contrails for two flight altitudes, which here is equivalent to two different background temperatures. The relative humidity with respect to ice was kept constant; a value of 110% was used. It is found that LH2 contrails are optically thinner than their kerosene counterparts owing to much lower number density of ice crystals in the LH2 contrails than in the kerosene contrails but similar amounts of ice mass. The latter is controlled by ambient humidity. However, the sedimentation in the LH2 contrails is not significantly stronger than the sedimentation in the kerosene contrails although the average crystal sizes in LH2 contrails are 4--6 times larger than in the corresponding kerosene contrail. Additionally, the sensitivity of the LH2 contrail properties to variations in the background aerosol distribution is investigated. We find that by increasing the aerosol density by 4, an order of magnitude difference in mean optical thickness results; the LH2 contrail will nevertheless be optically thinner than the corresponding kerosene contrail, as the number of ice crystals that form will be fewer.