Accurate estimates of compositional-dependent microemulsion viscosities are critical to model flow in surfactant-polymer floods. Microemulsions are mixtures of oil, water and surfactant with complex internal structures and interaction forces between components. This paper develops a physics-based microemulsion viscosity model at low shear rate for compositional variations within a fixed ternary surfactant-brine-oil system. Our proposed model generates continuous viscosities for the entire compositional space with honored physical limits. First, binary water-surfactant and oil-surfactant viscosities variations along the axes of the ternary diagram are captured. Second, viscosity peaks at the "percolation locus" are reproduced, where the percolation locus is defined by hypothetical single-phase compositions within the ternary diagram. Last, end-point viscosities of pure water and oil on the apex of the ternary diagram are honored. The results show that the new model fits and predicts single phase microemulsion viscosities in ternary compositional space with acceptable accuracy (R2> 0.75) for a challenging three pseudocomponent system of isooctane, decane, and cyclohexane mixed with water and surfactant. The first-of-its-kind viscosity model can be coupled with any microemulsion phase behavior equations of state, such as that based on HLD-NAC.