  We calculate the branching ratio of the non-resonant $B \to D^-
\pi^+\pi^+\pi^- $ decay using a simple model based on the framework of the
factorization approach. In naive factorization approach, there are only tow
tree diagrams for this decay mode. In the first diagram, the matrix element of
decay mode is factorized into a $B\to D$ form factor multiplied by a $3\pi$
decay constant and in the second diagram, the matrix element is factorized into
a $B\to D\pi$ form factor multiplied by a $2\pi$ decay constant, We assume that
in the rest frame of B meson, the $D$ meson remains stationary, so we obtain
the value $(3.47\pm0.14)\times 10^{-3}$ for the branching ration of the $B \to
D^- \pi^+\pi^+\pi^- $ decay mode, while the experimental results are
$(3.9\pm1.9)\times10^{-3}$.
