In this article we study closed inflationary universe models by using a tachyonic field theory. We determine and characterize the existence of a universe which has Ω>1 and which describes a period of inflation. We find that the considered models are less restrictive compared to the standard ones with a scalar field. We use recent astronomical observations to constrain the parameters appearing in the model. The results obtained are compared to those found in the standard scalar field inflationary universes.