The breakup of a laminar liquid jet into drops in non-Newtonian immiscible liquid systems has been studied using a two-dimensional cylindrical axisymmetric front-tracking/finite difference method with the Carreau-Yasuda model for non-Newtonian viscosities. For co-flow condition, where the continuous phase flows with the same velocity as the jet injection velocity, the lengths of the jet and the sizes of the drops are in good agreement between numerical simulations and experiments reported previously. Non-Newtonian effects are discussed by visualizing the distribution of viscosity. The breakup length of the jet becomes large when shear thinning occurs inside the jet, while the jet becomes short when shear thinning occurs in a continuous phase.