  In this paper we calculate the weak form factors of the decays $B_c(B)\to
Dl\tilde\nu$ by using the chiral current correlator within the framework of the
QCD light-cone sum rules (LCSR). The expressions of the form factors only
depend on the leading twist distribution amplitude (DA) of the $D$ meson. Three
models of the $D$-meson distribution amplitude are employed and the calculated
form factor $F_{B_c\to D}(0)$ is given. Our prediction, by using the $D$-meson
distribution amplitude with the exponential suppression at the end points, is
compatible with other approaches, and favors the three-points sum rules (3PSR)
approach with the Coulumb corrections included.
