  The generalized teleparallel gravity has been suggested to explain the
present cosmic acceleration of the universe. In this paper, we take spatially
homogenous and anisotropic Bianchi type $I$ universe in the framework of $F(T)$
gravity. The behavior of accelerating universe is investigated for three purely
kinetic k-essence models. We explore equation of state parameter and
deceleration parameter for these k-essence models. It is found that all these
models exhibit quintessence behavior of the universe.
