Fractal Dimension is one of the most important properties of rivers. There are three simple and accurate methods for finding fractal dimension in this paper. These methods were applied to 32 Taiwan river sections. The result is the fractal dimension ranging from 1.02 to 1.21 for compass method, from 1.03 to 1.22 for grid method, and from 1.02 to 1.16 for component method. We shall pay special attention to the component method, because the direction of coordinate system, the upper limit, and the lower limit will affect the fractal dimension.