In this paper we study a gravitational theory in which tachyons play the role of a scalar field. Also, nonminimal derivative coupling between tachyons and the Einstein tensor is considered in the model. We show that at the initial time, tachyon field behavior is exponential and its behavior at late times is liner in cosmic time. We investigate the asymptotic behavior of scale factor a(t) = eα(t) and show that in the limit t → ∞ it is impossible to have a constant and the model has an initial cosmological singularity (i.e., a ∝ (t – ti)2/β) in the limit t – t
