  In this note, we calculate the branching ratio of B_c\to J/\psi K in the
framework of perturbative QCD approach based on k_T factorization. This decay
can occur only via tree level diagrams in the Standard Model. We find that the
branching ratio of B_c\to J/\psi K is about (1-3)\times10^{-4}. The large
branching ratio and the clear signals of the final states make the measurement
of B_c\to J/\psi K easily at LHC-b experiments.
