In this paper, the Korteweg-de Vries-Burgers' (KdVB) equation is solved numerically by a new differential quadrature method based on quintic B-spline functions. The weighting coefficients are obtained by semi-explicit algorithm including an algebraic system with five-band coefficient matrix. The L-2 and L-infinity error norms and lowest three invariants I-1, I-2 and I-3 have computed to compare with some earlier studies. Stability analysis of the method is also given. The obtained numerical results show that the present method performs better than the most of the methods available in the literature.