An air bubble rising in a non-Newtonian fluid (shear thinning/thickening) has been numerically studied using a volume-of-fluid (VoF) approach in the axisymmetric regime. The governing equations consist of mass and momentum conservation, coupled to an equation for the volume fraction of the non-Newtonian fluid, which is modelled using the Carreau–Yasuda model. The solver is validated extensively by performing grid convergence test and comparing with the earlier studies in the literature. A parametric study is conducted by varying the shear-thinning/thickening tendency of the surrounding fluid for different Gallilei and Eötvös numbers. The effect of these parameters is quantified in terms of their influence on the aspect ratio of the bubble, the position of the center of gravity and the bubble shape as these evolve over time. We found that increasing the shear thinning tendency increases the rise velocity, and reduces the deformations of the bubble. The deformation of the bubble is also enhanced for higher Gallilei number and low Eötvös number. © 2016 Elsevier B.V.