  We study the exclusive semileptonic rare $B_c^+ \to D^+ \nu \bar{\nu}$ decay
in the framework of light-cone quark model. The transition form factors
$f_{+}(q^2)$ and $f_{T}(q^2)$ are evaluated in the time-like region using the
analytic continuation method in $q^{+} = 0$ frame. The analytic solutions of
these form factors are compared with the results obtained from the double pole
parametric form. The branching ratio for $B_c^+ \to D^+ \nu \bar{\nu}$ decay is
calculated and compared with the other theoretical model predictions. The
predicted results in this model can be tested at the LHCb experiments in near
future which will help in testing the unitarity of CKM quark mixing matrix,
thus, providing an insight into the phenomenon of CP violation.
