  With the one-boson-exchange model, we study the interaction between the
S-wave $D^{(*)}/D^{(*)}_s$ meson and S-wave $B^{(*)}/B^{(*)}_s$ meson
considering the S-D mixing effect. Our calculation indicates that there may
exist the $B_c$-like molecular states. We estimate their masses and list the
possible decay modes of these $B_c$-like molecular states, which may be useful
to the future experimental search.
