The Boltzman equation in a rarefied Taylor-Quette flow regime is solved by using the New Monte Carlo method which applies equilibrium conditions in each time step. The results obtained from this method are compared with those form the usual Direct Simulation Mont Carlo (DSMC) method. This comparesion shows good agreement between the two sets of results , whereas, the number of collisions and CPU usage time in the suggested method, as compared to the DSMC method, show a significant decrease.