We study the B c → ψð2SÞ K, η c ð2SÞ K, ψð3770Þ K decays with perturbative QCD approach based on k T factorization. The new orbitally excited charmonium distribution amplitudes ψð1 3 D 1 Þ based on the Schrödinger wave function of the n ¼ 1, l ¼ 2 state for the harmonic-oscillator potential are employed. By using the corresponding distribution amplitudes, we calculate the branching ratio of B c → ψð2SÞ K, η c ð2SÞ K, ψð3770Þ K decays and the form factors A 0;1;2 and V for the transition B c → ψð1 3 D 1 Þ. We obtain the branching ratio of both B c → ψð2SÞ K and B c → η c ð2SÞ K are at the order of 10 −5 . The effects of two sets of the S-D mixing angle θ ¼ −12°and θ ¼ 27°for the decay B c → ψð3770Þ K are studied first in this paper. Our calculations show that the branching ratio of the decay B c → ψð3770Þ K can be raised from the order of 10 −6 to the order of 10 −5 at the mixing angle θ ¼ −12°, which can be tested by the running LHC-b experiments.