In the light of recent observations which point to an open universe (Omega(0) < 1), we construct an open singularity-free cosmological model by reconsidering a model originally constructed for a closed universe. Our model starts from a nonsingular state called prematter, governed by an inflationary equation of state P = (gamma(p) - 1)rho where gamma(p) (similar or equal to10(-3)) is a small positive parameter representing the initial vacuum dominance of the universe. Unlike the closed models universe cannot be initially static hence, starts with an initial expansion rate represented by the initial value of the Hubble constant H(0). Therefore, our model is a two-parameter universe model (gamma(p), H(0)). Comparing the predictions of this model for the present properties of the universe with the recent observational results, we argue that the model constructed in this work could be used as a realistic universe model.