In the present paper, we suggest a convenient model for the vector $ρ$-meson longitudinal leading-twist distribution amplitude $ϕ_{2;ρ}^\|$, whose distribution is controlled by a single parameter $B^\|_{2;ρ}$. By choosing proper chiral current in the correlator, we obtain new light-cone sum rules (LCSR) for the $B\toρ$ TFFs $A_1$, $A_2$ and $V$, in which the $δ^1$-order $ϕ_{2;ρ}^\|$ provides dominant contributions. Then we make a detailed discussion on the $ϕ_{2;ρ}^\|$ properties via those $B\toρ$ TFFs. A proper choice of $B^\|_{2;ρ}$ can make all the TFFs agree with the lattice QCD predictions. A prediction of $|V_{\rm ub}|$ has also been presented by using the extrapolated TFFs, which indicates that a larger $B^{\|}_{2;ρ}$ leads to a larger $|V_{\rm ub}|$. To compare with the BABAR data on $|V_{\rm ub}|$, the longitudinal leading-twist DA $ϕ_{2;ρ}^\|$ prefers a doubly-humped behavior.

7 pages, 3 figures. Discussions improved and references updated. To be published in Phys.Lett.B