Despite having the advantage of a secondary flow pattern in coiled tubes, a very high Dean number is required to induce significant mixing in helical coils, usually implying high shear rates. At very high shear rates, polymer fluids with long molecular chains can be damaged. Therefore, in this study, we investigate the enhancement of mixing of a viscoelastic fluid in a coiled tube at low Dean numbers using the concept of a coiled flow inverter (CFI). Viscoelastic flow simulations were performed for CFIs of different curvature ratios, by changing the coil diameter, for a range of Weissenberg numbers (Wi) 0-125. An analytical method using velocity streamlines to quantify mixing is presented. The pressure drop per unit length increases with increasing Wi number. A more efficient mixing is predicted in the CFI, when compared with a helix of the same curvature ratio for all flow conditions. The mixing in the CFI is improved with an increase in flow rates (Wi). The mixing is enhanced at every bend because of flow inversion in the CFI.