The application of Taylor's dispersion theory to non-Newtonian laminar dispersion in a circular curved pipe wrapped in a coil is discussed. An analytical expression for the dispersion coefficient in laminar flow under two conditions, viz. Dean's constraint and relaxing Dean's constraint, is discussed along with system parameters. The present expression of dispersion coefficient under two different conditions reduces to the reported results in the literature for Newtonian fluids. The effect of power law index in combination with other process parameters on dispersion coefficient is studied. It is found that the dispersion coefficient decreases with decrease in power law index, and that it decreases with increase in Reynolds number and Schmidt number at a fixed curvature ratio.