In　this　paper,　we　prove　the　almost　global　existence　of　classical　solutions　to　the　3D　Prandtl　system　with　the　initial　data　which　lie　within　ε　of　a　stable　shear　flow.　Using　anisotropic　Littlewood-Paley　energy　estimates　in　tangentially　analytic　norms　and　introducing　new　linearly-good　unknowns,　we　prove　that　the　3D　Prandtl　system　has　a　unique　solution　with　the　lifespan　of　which　is　greater　than　exp　(ε−　1/　log　(ε−　1)).　This　result　extends　the　work　obtained　by　Ignatova　and　Vicol　(Arch.　Ration.　Mech.　Anal.　2:809–848,　2016)　on　the　2D　Prandtl　equations　to　the　three-dimensional　setting.　©　2019,　Springer　Nature　B.V.