Artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. Despite the merit, this algorithm can only solve problems with one objective. To solve complex multi-objective optimization problems, including engineering design problems, a multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. In addition, a non-dominated sorting strategy is merged with MOAHA to construct a solution update mechanism, which effectively refines Pareto optimal solutions for improving the convergence of the algorithm. The superior results over 7 competitors on 28 benchmark functions in terms of convergence, diversity and solution distribution are demonstrated with a suite of comprehensive tests. The MOAHA algorithm is also applied to 5 real-world engineering design problems with multiple objectives, demonstrating its superiority in handling challenging real-world multi-objective problems with unknown true Pareto optimal solutions and fronts. The source code of MOAHA is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/113535-moaha-multi-objective-artificial-hummingbird-algorithm and https://seyedalimirjalili.com/aha.