We present a CFD based model to understand the Taylor bubble behavior'in Newtonian and non-Newtonian liquids flowing through a confined co-flow microchannel. Systematic investigation is carried out to explore the influence of surface tension, inlet velocities, and apparent viscosity on the bubble length, shape, velocity, and film thickness around the bubble. Aqueous solutions of carboxymethyl cellulose (CMC) with different concentrations are considered as power law liquid to address the presence of non-Newtonian continuous phase on Taylor bubble. In all cases, bubble length was found to decrease with increasing Capillary number, inlet gas liquid velocity ratio, and CMC concentration. However, bubble velocity increased due to increasing liquid film thickness around the bubble. At higher Capillary number and inlet velocity ratio, significant changes in bubble shapes are observed. With increasing CMC concentration, bubble formation frequency and velocity increased, but length decreased.