In this Letter, we consider a model of tachyon with a non-minimal coupling to gravity and study its cosmological effects. Regarding inflation, we show that only for a specific coupling of tachyon to gravity this model satisfies observations and solves various problems which exist in the single and multi tachyon inflation models. But noting in the string theory the coupling coefficient of tachyon to gravity is of order g s , which in general is very small, we can hardly expect that the non-minimally coupling of tachyon to gravity could provide a reasonable tachyon inflation scenario. Our work may be a meaningful try for the cosmological effect of tachyon non-minimally coupled to gravity.