Recently various evolutionary approaches have been developed for multi-objective optimization. Most of them take Pareto dominance as their selection strategy and do not require any preference information. However these algorithms cannot perform well on problems involving many objectives. By introducing preferences among different criteria, a multi-objective concordance genetic algorithm (MOCGA) is proposed to deal with the problems in the paper. As the number of objectives to be simultaneously optimized increases, the weak dominance is used to compare among the individuals with decision-maker's information. It is proven that the algorithm can guarantee the convergence towards the global optimum. Experimental results of the multi-objective optimization benchmark problems demonstrate the validity of the new algorithm.