We develop a lattice Boltzmann model for compound Burgers-Korteweg-de Vries (cBKdV) equation. By properly treating dispersive term u_xxx and applying Chapman-Enskog expansion, the governing equation is recovered correctly from lattice Boltzmann equation and local equilibrium distribution functions are obtained. Numerical experiments show that our results agree well with exact solutions and have better numerical accuracy compared with previous numerical results. This hence indicates that the model is satisfactory and efficient.