A　scheme　is　proposed　for　the　generation　of　two-atom　maximally　entangled　states　and　multi-atom　maximally　entangled　states　of　W　class.　The　scheme　is　based　on　the　simultaneous　resonant　interaction　of　atoms　with　a　single-mode　cavity　field.　It　does　not　require　accurate　adjustment　of　the　interaction　time.　The　time　needed　to　complete　the　generation　does　not　increase　with　the　number　of　the　atom.　©　International　Academic　Publishers.