A non-homogeneous cosmological model which represents a fractal distri
bution of matter is given. For relatively short time the fractal distr
ibution is obvious. As time increases it tends to the k = 0 Robertson-
Walker metric. Thus it agrees with the known results of gravitational
red shift, Hubble's law etc. It also agrees with the recent findings o
f Coleman et al. that the universe has a kind of fractal symmetry. Our
model is a special choice of Tolman's solutions. It is shown that it
solves the particle horizon problem.