The diffusiophoresis of charged hydrophobic nanoparticles (NPs) governed by an imposed ionic concentration gradient is analysed. The main objective is to elucidate the impact of the laterally mobile adsorbed surface ions at the interface on the propulsion of the hydrophobic NPs in diffusiophoresis. In addition, the dielectric polarization due to the difference in dielectric constant between the NPs and the suspension medium is also considered. The mobile surface ions create a friction as well as an electric force at the hydrophobic surface, which leads to a modification of the slip velocity condition and the slip length. We obtain an exact numerical solution of the governing electrokinetic equations in their full form by adopting a control volume formulation. The numerical model is supplemented by analytical solutions derived based on the Debye–Hückel linearization. We find that the lateral mobility of the surface ions obstruct the coions to diffuse from the higher concentration side to the lower concentration side, which results in a repulsive force to the particle leading to the occurrence of a negative mobility. Based on the numerical results and analytical solutions, we have shown that for a fully mobile surface charge, the diffusiophoresis of a hydrophobic NP is identical to the diffusiophoresis of a liquid droplet whose viscosity is related to the slip length of the hydrophobic particle. We establish that the dielectric polarization enhances the velocity of a hydrophobic particle, which has potential applications in the practical context.