Fractal geometry, due to its ability for describing natural objects better than Euclidean geometry, has attracted great interests ever since Mandelbrot presented the concept of fractals in 1975. This paper investigates the fractal characteristic of eight individual river plan forms in Taiwan. Analyzed using the Richardson plot, these rivers have sinuosity fractal dimensions ranging from 1.08 to 1.28, with a mean 1.19 and transition zones in the plots found to be curves, not sharp inflections. The channel width is found to be about an order less than the value of the lower cut-off in the plots. A model for estimation of the river channel width and its bed slope is proposed. Through a case study, this paper also discusses the length-area relationship.