In this article, we propose an evolutionary algorithm based on layered prediction (LP) and subspace-based diversity maintenance (SDM) for handling dynamic multiobjective optimization (DMO) environments. The LP strategy takes into account different levels of progress by different individuals in evolution and historical information to predict the population in the event of environmental changes for a prompt change response. The SDM strategy identifies gaps in population distribution and employs a gap-filling technique to increase population diversity. SDM further guides rational population reproduction with a subspace-based probability model to maintain the balance between population diversity and convergence in every generation of evolution regardless of environmental changes. The proposed algorithm has been extensively studied through comparison with five state-of-the-art algorithms on a variety of test problems, demonstrating its effectiveness in dealing with DMO problems.