A　totalk-coloring　of　a　graph　G　is　a　coloring　of　V(G)∪E(G)　using　k　colors　such　that　no　two　adjacent　or　incident　elements　receive　the　same　color.　The　total　chromatic　number　χ″(G)　is　the　smallest　integer　k　such　that　G　has　a　total　k-coloring.　Let　G　be　a　planar　graph　with　maximum　degree　Δ(G)　and　without　6-cycles.　In　this　paper,　it　is　proved　that　χ″(G)=　Δ(G)+1　if　Δ(G)＜5　and　G　contains　no　4-cycles,　or　Δ(G)＜6　and　G　contains　no　5-cycles.　©　2010　Elsevier　B.V.　All　rights　reserved.