Dispersion is studied on a two-dimensional hierarchical pore network with a power-law distribution of conductances, i.e., P(g) approximately g(mu-1), with gepsilon(0,1), and mu is the disorderliness parameter (mu > 0). A procedure for computing tracer dispersion transport on hierarchical networks was developed. The results show that the effective diffusion coefficient of the network scales similarly as conduction on the same lattice. This means that the disorder length scales for conduction and diffusion processes are the same, and can be predicted from percolation theory. The dispersivity, xi identical with D(||)/U, was found to diverge rapidly as mu-->0. The result is in agreement with the model developed by Bouchaud and Georges (C.R. Acad. Sci. (Paris) 307 1431, 1988). A limiting value of mu approximately 0.45 was found, below which the convection-dispersion equation is no longer valid.