A friction factor correlation for laminar, hydrodynamically fully developed pipe flows of shear-thinning non-Newtonian fluids is derived through analysis and asymptotic considerations. The specific non-Newtonian fluid model used is the extended modified power law model, which is functionally equivalent to the Cross model, and spans the entire shear rate range from the low to the high shear rate Newtonian regions, including the intermediate power law region. The friction factor correlation is a function of three dimensionless parameters and has an explicit form, making it well-suited to design calculations. The overall accuracy of the correlation is 6.6%, though it is much better than this in most cases. Graphical results for the correlation, and deviations with respect to high-accuracy numerical calculations are presented and discussed.