In this paper, we propose a new selection mechanism based on the maximin fitness function and a technique based on Euclidean distances between solutions to improve the diversity of the population in objective function space. Our new selection mechanism is incorporated into a multi-objective evolutionary algorithm (MOEA) which uses the operators of NSGA-II (crossover and mutation) to generate new individuals, giving rise to the so-called “Maximin-Distances Multi- Objective Evolutionary Algorithm (MD-MOEA)”. Our MD-MOEA is validated using standard test functions taken from the specialized literature, having three to six objective functions. MD-MOEA is compared with respect to MC-MOEA (which is based on the maximin fitness function and a clustering technique), MOEA/D using Penalty Boundary Intersection ( PBI), which is based on decomposition, and SMS-EMOA-HYPE (a version of SMS-EMOA that uses a fitness assignment based on the use of an approximation of the hypervolume indicator). Our preliminary results indicate that our MD-MOEA is a good alternative to solve multi-objective optimization problems having both low dimensionality and high dimensionality in objective function space because it obtains better results than MC-MOEA and MOEA/D in most cases and it is competitive with respect to SMS-EMOA-HYPE (in fact, it outperforms SMS-EMOA-HYPE in problems of high dimensionality) but at a much lower computational cost.