The Try TV on Us scheme is running on the movie and TV streaming service's site until February 11 and allows customers to watch as many as 28 episodes during the promotional period.
blinkbox has secured a deal with studios meaning that its users can purchase a sample episode from some of the most popular and critically acclaimed shows on UK and Us television for free.
The full list of shows included in the scheme are:
Hell on Wheels
How I Met Your Mother
Inspector George Gently
Low Winter Sun
Sons of Anarchy season 5
The Field of Blood