In this research work, we assumed that the densities of each component in a mixture are linearly distributed across the interface between the coexisting vapor and liquid phases, and we developed a linear gradient theory model for computing interfacial tensions of mixtures, especially mixtures containing supercritical methane, argon, nitrogen, and carbon dioxide gases at high pressure. With this model it is unnecessary to solve the time-consuming density profile equations of the gradient theory model, The model has been tested on a number of mixtures at low and high pressures. The results show excellent agreement between the predicted and experimental IFTs at high and moderate levels of IFTs, while the agreement is reasonably accurate in the near-critical region as the used equations of state reveal classical scaling behavior, To predict accurately low IFTs (sigma < 0.1 mN/m), an equation of state with proper scaling behavior at the critical point is at least required.