Using a set of similarity transformation, the equations governing unmagnetic collisionless warm dusty plasma are reduced to an ordinary differential equation and the analytical solutions are obtained under quasi-neutrality condition for the adiabatic and isotherm cases, respectively.Furthermore, the effects on the distribution of dust grains from the factors, such as the dust temperature, the charge number and the thickness of dust grain, are investigated with the data presented by reference in the adiabatic case.The results show that large number of dust grains are distributed on the edge of the space time and there is a little even none in the center of the space time, furthermore, the dust grains with higher temperature, more charge number and the higher rate of dust number density to ion number density are apt to distribute on the edge of the space time.