Mars experienced a dynamo process that generated a global magnetic field ~4.3–3.6 Ga. The cessation of this dynamo strongly impacted 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 K. Our results show that a Martian core with 16 wt% sulfur has a thermal conductivity of ~19 to 32 W m^-1 K^-1 from its top to the center, much higher than previously inferred from electrical resistivity measurements. Our modelled 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, significantly contributing to cessation of Martian dynamo.