Analysis of micro-Couette flow and heat transfer is carried out using the Burnett equations. The generalized differential quadrature (GDQ) method is used to obtain the numerical solutions. The results show that the effect of the rarefaction is significant on velocity, temperature, pressure and non-dimensional parameter Pr . E for Kn greater than or equal to 0.1. The relationships between the shear stress, heat flux and Kn number are obtained. The solution of the Burnett equations is superior than that of the Navier-Stokes equations at the relatively high Kn number in the slip flow regime. However, it is impossible to extend the Burnett equations to the entire transition flow regime.