We develop the second-order Monte Carlo wavefunction (MCWF) approach to the exciton dynamics of molecular aggregate systems composed of dipole-coupled two-state monomers. The explicit form of Lindblad operator, which is indispensable for applying the MCWF approach, for population relaxation among exciton states is derived based on the quantum master equation involving weak exciton-phonon coupling. The exciton migration behaviors obtained by the MCWF approach are turned out to coincide with those by the conventional master equation approach, indicating the high potential of the MCWF approach to the dissipative exciton dynamics of extended molecular aggregates or supermolecules. (c) 2005 Elsevier B.V. All rights reserved.