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In this paper, we apply a new theorem which was proven by Lu et al. ͓"Attractors for non-autonomous 2D Navier-Stokes equations with normal external forces," Discrete Contin. Dyn. Syst. 8, 701 ͑2005͔͒ to nonautonomous two-dimensional space periodic Navier-Stokes equation. We obtain the existence of the uniform attractor in D͑A͒ which is the domain of the Stokes operator A with periodic boundary conditions if external forces f͑t͒ are a normal function in L loc 2 ͑R ; H 1 ͒. The uniform attractor attracts all bounded subsets of D͑A͒ in the norm of D͑A͒.

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