We investigate the internal flow pattern of an evaporating droplet using tomographic particle image velocimetry (PIV) when the contact line non-uniformly recedes. We observe a three-dimensional azimuthal vortex pair while the contact line non-uniformly recedes and the symmetry-breaking flow field is maintained during the evaporation. Based on the experimental results, we show that the vorticity magnitude of the internal flow is related to the relative contact line motion. Furthermore, to explain how the azimuthal vortex pair flow is created, we develop a theoretical model by taking into account the relation between the contact line motion and evaporating flux. Finally, we show that the theoretical model has a good agreement with experimental results.