Diffusioosmosis is the deterministic fluid motion over a surface due to a solute concentration gradient. Current theories of diffusioosmosis have predicted separately the effects of channel surface hydrophobicity and ion-ion electrostatic correlations in electrolytes on diffusioosmosis. However, a predictive model that accounts for the coupled effects of surface hydrophobicity and ion-ion electrostatic correlations is lacking. Here, we develop a mathematical model to compute the diffusioosmotic mobility of an electrolyte in a hydrophobic channel. We analyze how the channel surface hydrophobicity and the electrolyte ion-ion electrostatic correlations together affect the diffusioosmotic flow. The present model can be used to understand and predict diffusioosmosis in a broad range of applications, including colloidal species separation, enhanced oil recovery, and nanoparticle drug delivery.