In　this　paper,　the　problem　of　horizontal　path　following　of　a　small　fixed-wing　unmanned　aerial　vehicle　(UAV)　is　studied　based　on　the　combined　kinematic/dynamic　model.　First,　a　stable　kinematic　path　following　control　law　is　designed.　Second,　the　backstepping　technique　is　applied　to　derive　the　roll　angle　command　by　considering　the　closed-loop　roll　dynamics.　The　stability　of　the　corresponding　nonlinear　system　is　guaranteed　by　Lyapunov　stability　arguments.　Third,　two　key　parameters　of　the　control　law　which　will　influence　the　path　following　performance　have　been　analyzed.　Two　fuzzy　logic　based　controllers　have　been　designed　to　optimize　the　parameters　to　improve　the　path　following　performance　(PFC_FL),　where　the　stability　of　the　corresponding　nonlinear　system　is　still　kept.　The　simulations　of　square　and　circular　paths　following　control　of　an　Aerosonde　UAV　have　been　studied.　The　path　following　performances　of　the　proposed　control　law　with　parameter　fixed　(PFC),　PFC_FL　method,　vector　field　(VF)　method,　and　pure　pursuit　with　light-of-sight　(PLOS)　method　were　compared.　The　proposed　PFC_FL　method　can　make　the　UAV　have　the　longest　length　of　corresponding　effective　flight　path　and　the　shortest　total　convergence　time.　The　PFC_FL　can　also　have　much　smaller　error　overshoots　than　those　by　using　the　method　PFC　during　route　switching.　©　2023,　ICROS,　KIEE　and　Springer.