Monarch Butterfly Optimization (MBO) is a meta-heuristic algorithm proposed in 2015 to simulate the migration behavior of monarch butterflies. There are two problems in the MBO algorithm when dealing with high-dimensional problems: It is easy to fall into local optimum, and the offspring generated by migration operators are greatly influenced by their parents. For these reasons, we propose a new algorithm, Monarch Butterfly Optimization with a Logistic Chaotic Map (LCMMBO). It uses a Logistic chaotic map to disturb the optimal solution and optimizes the offspring transfer mode in the migration operators. These operations respectively aim to enhance the ability to jump out of the local optimum and the ability of global search. The simulation results show that, in the case of handling high-dimensional optimization problems, the new algorithm enjoys excellent robustness and a strong ability to jump out of the local optimum.