We describe aMonte Carlo method for simulation of vapour-liquid phase coexistence in size-asymmetrical Lennard-Jones ( LJ) binary mixtures. The method incorporates the Solvent Repacking Monte Carlo ( SRMC) approach, which offers efficient trial moves for the exchange of a large particle for several small particles, into the Gibbs Ensemble Monte Carlo ( GEMC) method. SRMC yields a significant efficiency improvement in simulation of dilute large species mixtures at low temperature compared to the original GEMC method with identity exchange moves. Vapor-liquid phase diagrams are reported for LJ mixtures with a diameter ratio sSS : sLL of 1: 2 with well depth ratios SS : LL = 1.2, 1.5 and 2, producing spindle-type, azeotrope and closed loop types of phase diagram, respectively.