In this paper, a novel learnable population filter is proposed to solve the dynamic multi-objective problems (DMOPs), whose main idea is to pick out potential valuable individuals in the changing situation via the trained filter to facilitate the population convergence in a new environment. In particular, by selecting training samples from three different optional pools, rich information in the previous searching experiences can be sufficiently used to cope with the dynamic behaviors in DMOPs, thereby handling the imperfect history data availability caused by the environmental uncertainty to some extents. Then, the screened population in the new environment, which is regarded to have reliable quality that benefits accelerating the evolution, is used to initialize the static optimizer. In addition, partial random solutions are employed as supplement to the initial population to further enhance the diversity. It is shown from the benchmark evaluations that the proposed method outperforms some other popular algorithms on both convergence and diversity by seamlessly combining the mainstream strategies in dealing with the dynamic behaviors, which is a competitive method that conforms to the novel evolutionary transfer optimization (ETO) trend. Moreover, effectiveness of the core components is validated through extensive ablation studies, which brings a new sight in developing the learnable DMOP solvers.