We　consider　the　fully　implicit　treatment　for　the　nonlinear　term　of　the　Allen–Cahn　equation.　To　solve　the　nonlinear　problem　efficiently,　the　two-level　scheme　is　employed.　We　obtain　the　discrete　energy　law　of　the　fully　implicit　scheme　and　two-level　scheme　with　finite　element　method.　Also,　the　convergence　of　the　two-level　method　is　presented.　Finally,　some　numerical　experiments　are　provided　to　confirm　the　theoretical　analysis.　©　2018　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group