  We derive the time-dependent dipolar Gross-Pitaevskii (GP) equation from the
N-body Schr{\"o}dinger equation. More precisely we show a norm approximation
for the solution of the many body equation as well as the convergence of its
one-body reduced density matrix towards the orthogonal projector onto the
solution of the dipolar GP equation. We consider the interpolation regime where
interaction potential is scaled like $N^{3\beta--1} w(N^\beta (x -- y))$, the
range of validity of $\beta$ depends on the stability of the ground state
problem. In particular we can prove the convergence on the one-body density
matrix assuming $\widehat{w} $\ge$ 0$ and $\beta < 3/8$.
