This paper regards UAV-assist aerial edge computing as a dynamic multi-objective optimization problem. In order to continuously track the the moving Pareto set, a new Holt-based prediction correction dynamic multi-objective evolutionary algorithm (HDMOEA) is proposed. It includes mainly three main strategies. Firstly, Wilcoxon signed-rank test method is employed to accurately detect environmental change, and the intensity of which is further detected by a new environment perception operator. Secondly, Holt-based prediction correction mechanism is constructed to predict the positions of individuals in the next time Window. The positions are corrected according to a reference point in order to enhance prediction accuracy and accelerate the search speed of the algorithm. Lastly, a new bi-mutation method is proposed used to maintaining the diversity of the population according to the intensity of environmental changes, thereby reduce the likelihood of the population falling into local optima. The proposed algorithm is compared with six state-of-the-art prediction dynamic multi-objective algorithms on the multiple benchmark test sets. The experimental results show that HDMOEA can faster continuous tracking Pareto Frontier, and obtain more accurate Pareto Frontier Set compared with other comparison algorithms.