The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms (MOEAs) lies a certain distance away from the decision makers’ preference information region. Therefore, we propose a multi-objective optimization algorithm, referred to as the double-grid interactive preference based MOEA (DIP-MOEA), which explicitly takes the preferences of decision makers (DMs) into account. First, according to the optimization objective of the practical multi-objective optimization problems and the preferences of DMs, the membership functions are mapped to generate a decision preference grid and a preference error grid. Then, we put forward two dominant modes of population, preference degree dominance and preference error dominance, and use this advantageous scheme to update the population in these two grids. Finally, the populations in these two grids are combined with the DMs’ information, and the preference multi-objective optimization interaction is performed. To verify the performance of DIP-MOEA, we test it on two kinds of problems, i.e., the basic DTLZ series functions and the multi-objective knapsack problems, and compare it with several different popular preference-based MOEAs. Experimental results show that DIP-MOEA expresses the preference information of DMs well and provides a solution set that meets the preferences of DMs, quickly provides the test results, and has better performance in the distribution of the Pareto front solution set.