The Kelvin–Helmholtz instability (KHI) occurs on the interface of gold cones and embedded fuels for fusion schemes with gold cones. The development of KHI on the inner surface of gold cones in the double-cone ignition scheme is investigated with two-dimensional radiation hydrodynamic simulations. It has been found that the colliding high-density fuel plasma between the tips of the two cones is spatiotemporally separated from the mixed gold ions from the inner surface of the gold cones due to the KHI. Furthermore, it is found that fuel layers coated on the inner surface of the cones can effectively mitigate the energy loss in the compression process. These results could provide a reference for fast ignition schemes with gold cones.