  In this paper, we consider $2+1$ dimensional gravitational theory including a
Dirac field that is minimally coupled to New Massive Gravity. We investigate
cosmological solutions of the field equations by using the self-interaction
potential form obtained by the existence of Noether symmetry. In this context,
we obtain cosmological solutions that corresponds to inflationary as well as
the oscillationary epochs of the universe. Moreover, we have seen that the
Dirac field behaves like a dark energy in these epochs of the universe.
