Centroidal Voronoi tessellation (CVT) and its extensions have a wide spectrum of applications including computational geometry, image processing, cellular biology and scientific visualization etc. In this paper, we propose the concept of the complete streamline and the CVT of streamlines, and then formulate the computation of CVT of complete streamlines as a continuous variational problem. To reduce the computing complexity, we present a simple, approximation method for solving this problem. Given a flow field and a number of complete streamlines, our method can optimize the placement of the streamlines so that the streamlines best approximate the geometric characteristics of the flow field. Experimental results show the effectiveness of our method for flow visualization, especially in terms of continuity and uniformity.