We model blood in a microvessel as an inhomogeneous non-Newtonian fluid, whose viscosity varies with hematocrit and shear rate in accordance with the Quemada rheological relation. The flow is assumed to consist of two distinct, immiscible and homogeneous fluid layers: an inner region densely packed with red blood cells, and an outer cell-free layer whose thickness depends on discharge hematocrit. We demonstrate that the proposed model provides a realistic description of velocity profiles, tube hematocrit, core hematocrit and apparent viscosities over a wide range of vessel radii and discharge hematocrits. Our analysis reveals the importance of incorporating this complex blood rheology into estimates of wall shear stress in micro-vessels. The latter is accomplished by specifying a correction factor, which accounts for the deviation of blood flow from the Poiseuille law.