In　2022,　Li　et　al.　[1]　proposed　a　quantum　secure　and　non-interactive　identity-based　aggregate　signature　protocol　from　lattices.　In　the　end　of　their　paper,　they　claimed　that　their　scheme　has　key　escrow　problem.　Based　on　this　fact,　we　improve　their　scheme　and　propose　a　lattice-based　certificateless　aggregate　signature　protocol　(L-CASP).　Furthermore,　our　scheme　has　same　signature　size　as　Li　et　al.　scheme　and　can　avoid　key　escrow　problem.　Finally,　we　prove　that　our　scheme　is　existentially　unforgeable　against　adaptive　chosen　message　attacks　(EUF-CMA)　under　type　I　adversary　and　a　type　II　adversary　in　the　random　oracle　model　(ROM).　©　ICST　Institute　for　Computer　Sciences,　Social　Informatics　and　Telecommunications　Engineering　2024.