  In $F(T)$ gravity theory, a Friedman-Robertson-Walker cosmological model with
$f$-essence where fermion field is non-minimally coupled with the gravitational
field is studied. Using the Noether symmetry approach the possible forms of
$F(T)$ gravity and the non-canonical fermionic lagrangian $K$ are determined.
Cosmological solutions of the condered models describing the accelerated and
decelerated periods of the universe are found.
