The　research　of　topic　trend　prediction　can　be　a　good　reference　for　maximizing　the　propagation　effects　of　network　advertisements　as　well　as　guiding　and　controlling　the　network　consensus.　This　paper　proposes　PTEP(the　Prediction　of　Topic　Energy　Peak)　method　to　model　the　life　cycle　of　a　topic　and　predicts　the　time　when　a　hot　topic　will　outbreak.　Firstly,　taking　the　number　and　the　authority　of　followers　and　the　interest　of　users　to　a　topic　into　consideration,　we　design　a　topic-related　user　authority　(TRUA)　algorithm　to　measure　the　authority　of　users.　Secondly,　we　calculate　the　energy　value　considering　both　the　tweets　and　users　authority　related　to　the　topic.　Thirdly,　we　measure　the　fluctuation　of　the　energy　value　based　on　wavelet　transformation.　Finally,　we　present　rules　to　predict　topic　trend.　Experimental　results　show　that　our　method　can　effectively　predict　the　peak　of　a　topic　in　advance　with　a　low　omission　rate.