  With the potential prospects of the ${\Upsilon}(1S)$ data samples at the
running LHC and upcoming SuperKEKB, the ${\Upsilon}(1S)$ ${\to}$ $B_{c}{\rho}$
weak decays are studied with the pQCD approach. It is found that (1) the lion's
share of branching ratio comes from the longitudinal polarization helicity
amplitudes; (2) branching ratio for the ${\Upsilon}(1S)$ ${\to}$ $B_{c}{\rho}$
decay can reach up to ${\cal O}(10^{-9})$, which might be hopefully measurable.
