In heavy oil displacement by gas, chemical, or water injection, severe instability can occur due to adverse mobility ratio, gravity or compositional effects. However, most analytical methods for estimation of relative permeability such as JBN, assume a stable front in the displacement. This implies that such methods cannot be applied to estimate relative permeability when the displacement is severely unstable. A common approach for estimation of relative permeability in displacement with instability involves the history matching of a 2D or 3D high resolution, fine scale models of the displacement. However, this is also impractical due to associated high computational cost. This work describes a fast methodology for the estimation of relative permeability functions in displacement with instability and compositional effect using multi coarse-scale models. It involves the history matching of a set of coarse grid models of the unstable displacement and correlating the parameter a relative permeability function (L.E.T) in order to estimate the relative permeability of the corresponding high-resolution model. By this approach, an attempt was made to resolve the fine-scale information without direct solution of the global fine-scale problem. Hence, an unstable displacement can be modelled using a coarse grid model which has a relatively lower computational cost. The results showed that the approach is three times faster, and required less than half the memory of a conventional method.