  Inspired by the recent LHCb measurements and forthcoming great potential on
$B_{c}$ meson, we study the exclusive $B_{c}$ ${\to}$ $B_{q}P$, $B_{q}V$ decays
with the perturbative QCD approach, where $q$ $=$ $u$, $d$, $s$; $P$ and $V$
denote the lightest pseudoscalar and vector $SU(3)$ nonet meson, respectively.
By retaining the quark transverse momentum, employing the Sudakov factors, and
choosing the typical scale as the maximum virtualities of the internal
particles, we calculate the $B_{c}$ ${\to}$ $B$ transition from factors, and
our results show that about 90\% contribution to form factors come from the
${\alpha}_{s}/{\pi}$ $<$ $0.3$ region. The contributions of penguin and
annihilation to branching ratios are very small due to the serious suppression
by the CKM factors. There is some hierarchy relations among the $B_{c}$ ${\to}$
$BP$, $BV$ decays. The branching ratios for $B_{c}$ ${\to}$ $B_{d,s}{\pi}$,
$B_{d,s}{\rho}$, $B_{s}K$ are large and could be measured by the running LHCb.
