  A modified form of non-locally corrected theory of gravity is investigated in
the context of cosmology and the Newtonian limit. This form of non-local
correction to classic Einstein-Hilbert action can be locally represented by a
triple-scalar-tensor theory in which one of the scalar degree of freedom is
phantom-like and the other two are quintessence-like. We show that there exists
a stable de Sitter solution for the cosmological dynamics if a suitable form of
potential function $V(\phi)$ (or equivalently, $f(R)$) is selected. However, no
matter what a potential function is selected, there is always an early time
repeller solution corresponding to a radiation dominated universe. Besides, the
equations for linear scalar perturbations are presented and it is shown that
the form of potential function $V(\phi)$ is stringently constrained by the
Solar system test, although the post-Newtonian parameter $\gamma$ is not
directly affected by this function.
