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.　©　2024　Beijing　University　of　Technology.　All　rights　reserved.