This paper presents a multi-objective evolutionary algorithm based on decomposition (MOEA/D) to design broadband optimal Yagi-Uda antennas. A multi-objective problem is formulated to achieve maximum directivity, minimum voltage standing wave ratio and maximum front-to-back ratio. The algorithm was applied to the design of optimal 3 to 10 elements Yagi-Uda antennas, whose optimal Pareto fronts are provided in a single picture. The multi-objective problem is decomposed by Chebyshev decomposition, and it is solved by differential evolution (DE) and Gaussian mutation operators in order to provide a better approximation of the Pareto front. The results show that the implemented MOEA/D is efficient for designing Yagi-Uda antennas.