We study the buoyancy-induced interpenetration of two immiscible fluids in a tilted channel by a two-phase lattice Boltzmann method using a non-ideal gas equation of state well-suited for two incompressible fluids. The method is simple, elegant and easily parallelizable. After first validating the code for simulating Rayleigh-Taylor instabilities in a unstably-stratified flow, we applied the code to simulate the buoyancy-induced mixing in a tilted channel at various Atwood numbers, Reynolds numbers, tilt angles, and surface tension parameters. The effects of these parameters are studied in terms of the flow structures, front velocities, and velocity profiles. For one set of parameters, comparisons have also been made with results of a finite volume method. The present results are seen to agree well with those of a finite volume method in the interior of the flow; however near the boundary there is some discrepancy. © 2011 Elsevier Ltd.