The pseudoplastic circular Couette flow (CCF) in annuli is investigated.The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study.The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids.Unlike the previous studies,where only the square of the shear rate term in the viscosity expression is considered to ease the numerical manipulations,in the present study,the term containing the quadratic power is also taken into account.The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices,known as the Taylor vortices.It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.