This paper is concerned with the system of equations that model incompressible non-Newtonian fluid motion with p-growth dissipative potential 1 ＋ 2n/n＋2 〈 p 〈 3 in R^n （n = 2,3）. Using the improved Fourier splitting method, we prove that a weak solution decays in L2 norm at the same rate as （1 ＋ t）^-n/4 as the time t approaches infinity.
