In this paper, we consider the multimodal multi-objective path planning (MMOPP) optimization, which is the main topic of a special session in IEEE CEC 2021. The MMOPP aims at finding all the Pareto optimal paths from a start area to a goal area on a grid map, while passing through several designated must-visit areas. We propose an efficient approach based on the multi-objective A* algorithm to exactly solve the MMOPP. Experiments are conducted on the official MMOPP test suite to evaluate the performance of the proposed approach. We also show the admissibility of the proposed approach so that the computational results can be used as the standard answers to the MMOPP test suite.