This paper discusses about the possibility of the adjoint eigenmode calculation for the Monte Carlo neutron transport problem with the application of the modified power method. The modified power method has been studied to simulate several forward eigenmodes at the same time by introducing a weight vector to one neutron. The adjoint eigenmodes are introduced in this paper by adopting the bi-orthogonal property of the forward and adjoint eigenmodes. The preliminary results based on the BEAVRS 3D whole core model are very encouraging. Further study about the theory and implementation issues will be done to improve the performance of the method.