The purpose of this work is obtain the numerical approximate solutions of the nonlinear modified Burgers’ equation (MBE) via the modified cubic B-spline (MCB) differential quadrature methods (DQMs). The accuracy and effectiveness of the methods are measured and reported by finding out error norms 𝐿2 and 𝐿∞. The present numerical results have been compared with some earlier studies and this comparison clearly indicates that the method is an outstanding numerical scheme for the solution of the MBE. A stability analysis has at the same time been given.