  We find some new exact cosmological solutions for the covariant
scalar-tensor-vector gravity theory, the so-called MOdified Gravity (MOG). The
exact solution of the vacuum field equations has been derived. Also, for non
vacuum cases we have found some exact solutions with the aid of the Noether
symmetry approach. More specifically, the symmetry vector and also the Noether
conserved quantity associated to the point-like Lagrangian of the theory have
been found. Also we find the exact form of the generic vector field potential
of this theory by considering the behavior of the relevant point-like
Lagrangian under the infinitesimal generator of the Noether symmetry. Finally,
we discuss the cosmological implications of the solutions.
