The present paper investigates the dimensionless dynamical continuity equation of perfect gas motion in gravitational field. Based on Π axiom of dimensional theory， self-similarity of perfect gas universe with gravity and a series of exact solutions of R(t) are deduced. Based on R(t)，a non-Euclidean homogeneous space-time coordinate system S(t,ξ，θ，φ) can be established. A perfect gas universe solution can be worked out， in which there is a constant density ρ， the velocity u value being zero， and there is a nonzero pressure p. In this solution， the red shift z represents the propagating distance r. When z is much less than 1， it is proportional to r (Hubbles law). The Robertson-Walker (k=-1) metric of normal universe model is obtained from homogeneous expanding coordinates， and the ratio of expanding rate HF to the Hubble constant H0 decreases notably as the value of z rises. It corresponds to the “universal accelerated expansion” observed in the spectrum of a high-red-shift supernova.