We study a one-field open inflationary model in a universe dominated by tachyon matter [1, 2]. We work in the scenario of the one-bubble universe where bubble formation is described by the Coleman-De Lucia (CDL) instanton . The conditions of existence and basic characteristics of the CDL instanton were determinated for the tachyon model using analytical and numerical approaches. Also, we study the Lorentzian regime, that is, the period of inflation after tunnelling has occurred. In particular we focus on the viability of the model in order to generate a consistent inflationary scenario, compatible with observations.