  In this paper, the cosmological dynamics of Brans-Dicke theory in which there
are fermions with a coupling to BD scalar field as well as a self-interaction
potential is investigated. The conditions that there exists a solution which is
stable and represents a late-time accelerated expansion of the universe are
found. The variable mass of fermions can not vanish exactly during the
evolution of the universe once it exists initially. It is shown that the
late-time acceleration depends completely on the self-interaction of the
fermionic field if our investigation is restricted to the theory with positive
BD parameter $\omega$. Provided a negative $\omega$ is allowed, there will be
another two class of stable solutions describing late-time accelerated
expansion of the universe.
