In this paper, a novel dynamic multi-objective optimization algorithm (DMOA) is proposed based on a designed hierarchical response system (HRS). Named as HRS-DMOA, the proposed algorithm mainly aims at integrating merits from the mainstream ideas of dynamic behavior handling (i.e., the diversity-, memory-, and prediction-based methods) so as to make flexible responses to environmental changes. In particular, by two pre-defined thresholds, the environmental changes are quantified as three levels. In case of a slight environmental change, the previous Pareto set-based refinement strategy is recommended, while the diversity-based re-initialization method is applied in case of a dramatic environmental change. For changes occurring in a medium level, the transfer-learning-based response is adopted to make full use of the historical searching experiences. The proposed HRS-DMOA is comprehensively evaluated on a series of benchmark functions, and the results show an improved comprehensive performance as compared with four popular baseline DMOAs in terms of both convergence and diversity, which also outperforms other two state-of-the-art DMOAs in 10 out of 14 testing cases, exhibiting the competitiveness and superiority of the algorithm. Finally, extensive ablation studies are carried out, and from the results, it is found that as compared with randomly selecting the response methods, the proposed HRS enables more reasonable and efficient responses in most cases. In addition, the generalization ability of the proposed HRS as a flexible plug-and-play module to handle dynamic behaviors is proven as well.