Abstract: The combination of high altitude platform (HAP) technology and multi-access edge computing (MEC) technology extends the deployment area of MEC servers from the ground to the air, breaks the limitations of traditional terrestrial MEC networks and provides users with ubiquitous computation offloading services. This survey conducts a review on the researches of computation offloading in HAP-based MEC. First, the HAP-based MEC network was analyzed from four aspects: advantages of HAP computing nodes, network components, network structures, main challenges and their coping techniques. Second, from the perspectives of graph theory, game theory, machine learning, federated learning and other theories, the computation offloading algorithms based on HAP were analyzed horizontally and compared vertically. Finally, the current problems of computation offloading technology in HAP-based MEC were pointed out and the future research directions of this technology are prospected.