In this paper, we have presented the cosmological model of the Universe that represents late time cosmic acceleration in torsion based gravitational theory, the $f(T)$ gravity. A well motivated parametrization for the Hubble parameter has been introduced and the free parameters involved are constrained using the cosmological datasets. With the constrained values of the free parameters, other geometrical parameters such as deceleration parameter, jerk parameter, and snap parameter are analyzed and confronted with the prescribed value of the cosmological observations. In addition, the dynamical parameters are analyzed in some non-linear form of $f(T)$ and the energy conditions are also studied and confirmed with the violation of the strong energy condition. The obtained cosmological model provides late time phantom behavior of the Universe.