There are many dynamic multi-objective optimization problems in real life. Once the environment changes, evolutionary algorithms are required to quickly track the moving Pareto front or Pareto set of optimization problems over time. We propose a classification-based multi-strategy prediction method (CMSP). Firstly, the approximate optimal solution obtained by optimization is used to detect the type of the Pareto set(PS) change: invariance, translation and others. Then, different coping strategies are adopted for different types of change: If type is invariance, the elite individual is retained and diversity is ensured; If it is translation, a time series is established for the center point of the optimal solution set, and the population is updated using the predictive gradient strategy, the predicted individuals are compared with the individuals retained from the old population to ensure the accuracy of the prediction; If it belongs to other situation, several time series are established for multiple special points to predict the location of individuals in the new environment. Finally, a population preservation strategy and a memory retrieval strategy are introduced, which is beneficial to more fully utilizing historical information. The experimental results show that the CMSP can perform dynamic multi-objective optimization well.