  The inclusive J/$\psi$ production in Pb-Pb collisions at the center-of-mass
energy per nucleon pair $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV, measured with the
ALICE detector at the CERN LHC, is reported. The J/$\psi$ meson is
reconstructed via the dimuon decay channel at forward rapidity ($2.5<y<4$) down
to zero transverse momentum. The suppression of the J/$\psi$ yield in Pb-Pb
collisions with respect to binary-scaled pp collisions is quantified by the
nuclear modification factor ($R_{\rm{AA}}$). The $R_{\rm{AA}}$ at
$\sqrt{s_{\rm{NN}}}$ = 5.02 TeV is presented and compared with previous
measurements at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV as a function of the centrality
of the collision, and of the J/$\psi$ transverse momentum and rapidity. The
inclusive J/$\psi$ $R_{\rm{AA}}$ shows a suppression increasing toward higher
$p_{\rm{T}}$, with a steeper dependence for central collisions. The
modification of the J/$\psi$ average $p_{\rm{T}}$ and $p_{\rm{T}}^{2}$ is also
studied. Comparisons with the results of models based on a transport equation
and on statistical hadronization are also carried out.
