Highways/railways often pass across slope areas and their embankments are often built on the slopes in permafrost regions. It is difficult to ensure the thermal stability of the embankments at the slopes due to the effect of slopes. To protect the underlying permafrost, the crushed-rock embankments are often used in the slope areas. Therefore, it is very necessary to explore the thermal state of crushed-rock embankments located on the slopes. In this study, we studied numerically the temperature characteristics of three kinds of crushed-rock embankments located on a slope under global warming, i.e. crushed-rock interlay embankment, crushed-rock interlayer-revetment embankment and crushed-rock base embankment. Numerical results indicate that the crushed-rock interlayer embankment and the crushed-rock interlayer-revetment embankment, located on a slope with a ratio of 1:3.73 (about 15° from the horizontal), cannot effectively eliminate the negative effect of climate warming and construction-induced warming, and the effect of slope is still obvious on the thermal stability of permafrost under the crushed-rock interlayer embankment. However, the crushed-rock base embankment can significantly reduce the temperature of underlying permafrost and keep the underlying permafrost table stable for a long term; furthermore, the ground temperatures under the long side slope are far lower than those under the short side slope, and this will be more advantageous to control the slide of the embankment located on a slope and increase its stability. We also find that the three kinds of embankments cannot all remove the thermal effects of construction from themselves in a short term. Generally speaking, the crushed-rock base embankment structure can be very advantageous to the thermal stability of the embankment on a slope.