Mars experienced a dynamo process that generated a global magnetic field ~4.3 (or earlier) to 3.6 billion years ago (Ga). The cessation of this dynamo strongly affected Mars' history and is expected to be linked to thermochemical evolution of Mars' iron-rich liquid core, which is strongly influenced by its thermal conductivity. Here, we directly measured thermal conductivities of solid iron-sulfur alloys to pressures relevant to the Martian core and temperatures to 1023 Kelvin. Our results show that a Martian core with 16 weight % sulfur has a thermal conductivity of ~19 to 32 Watt meter −1 Kelvin −1 from its top to the center, much higher than previously inferred from electrical resistivity measurements. Our modeled thermal conductivity profile throughout the Martian deep-mantle and core indicates a ~4- to 6-fold discontinuity across the core-mantle boundary. The core's efficient cooling resulting from the depth-dependent, high conductivity diminishes thermal convection and forms thermal stratification, substantially contributing to cessation of Martian dynamo. Mars' core is much more thermally conductive than previously inferred, which critically contributes to stop its early dynamo.