  In this work, we study the resonance contributions to the decay $B^-\to
K^+K^-\pi^-$, which is dominated by the scalar $f_0(980), K_0^*(1430)$, vector
$\rho(1450), \phi(1020), K^*(892)$ and tensor $f_2(1270)$ resonances. The
three-body decay is reduced to various quasi two-body decays, where the $B$
meson firstly decays into a resonance and a pion or a kaon, subsequently the
resonance decays into the other two final-state mesons. The quasi two-body
decays are calculated within the light-cone sum rule approach utilizing the
leading twist $B$ meson light-cone distribution amplitudes. Finally, the decay
branching fraction contribution from each resonance are calculated. Some of
them are compatible with experiment or previous theoretical works. Including
the effects of non-resonant and final-state interactions, we also evaluate the
total branching fraction.
