This paper studies the cosmology of accelerating expansion of the universe in modified teleparallel gravity theory. We discuss the cosmology of f(T, B) gravity theory and its implication to the new general form of the equation of state parameter wTB for explaining the late-time accelerating expansion of the universe without the need for the cosmological constant scenario. We examine the numerical value of wTB in different paradigmatic f(T, B) gravity models. In those models, the numerical result of wTB is favored with observations in the presence of the torsion scalar T associated with a boundary term B and shows the accelerating expansion of the universe.
