Paths planning of Unmanned Aerial Vehicles (UAVs) in a dynamic environment is considered a challenging task in autonomous flight control design. In this work, an efficient method based on a Multi-Objective Multi-Verse Optimization (MOMVO) algorithm is proposed and successfully applied to solve the path planning problem of quadrotors with moving obstacles. Such a path planning task is formulated as a multicriteria optimization problem under operational constraints. The proposed MOMVO-based planning approach aims to lead the drone to traverse the shortest path from the starting point and the target without collision with moving obstacles. The vehicle moves to the next position from its current one such that the line joining minimizes the total path length and allows aligning its direction towards the goal. To choose the best compromise solution among all the non-dominated Pareto ones obtained for compromise objectives, the modified Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is investigated. A set of homologous metaheuristics such as Multiobjective Salp Swarm Algorithm (MSSA), Multi-Objective Grey Wolf Optimizer (MOGWO), Multi-Objective Particle Swarm Optimization (MOPSO), and Non-Dominated Genetic Algorithm II (NSGAII) is used as a basis for the performance comparison. Demonstrative results and statistical analyses show the superiority and effectiveness of the proposed MOMVO-based planning method. The obtained results are satisfactory and encouraging for future practical implementation of the path planning strategy.