A　least　square　method　based　on　data　fitting　is　proposed　to　construct　a　new　lifting　wavelet,　together　with　the　nonlinear　idea　and　redundant　algorithm,　the　adaptive　redundant　lifting　transform　based　on　fitting　is　firstly　stated　in　this　paper.　By　variable　combination　selections　of　basis　function,　sample　number　and　dimension　of　basis　function,　a　total　of　nine　wavelets　with　different　characteristics　are　constructed,　which　are　respectively　adopted　to　perform　redundant　lifting　wavelet　transforms　on　low-frequency　approximate　signals　at　each　layer.　Then　the　normalized　l(P)　norms　of　the　new　node-signal　obtained　through　decomposition　are　calculated　to　adaptively　determine　the　optimal　wavelet　for　the　decomposed　approximate　signal.　Next,　the　original　signal　is　taken　for　subsection　power　spectrum　analysis　to　choose　the　node-signal　for　single　branch　reconstruction　and　demodulation.　Experiment　signals　and　engineering　signals　are　respectively　used　to　verify　the　above　method　and　the　results　show　that　bearing　faults　can　be　diagnosed　more　effectively　by　the　method　presented　here　than　by　both　spectrum　analysis　and　demodulation　analysis.　Meanwhile,　compared　with　the　symmetrical　wavelets　constructed　with　Lagrange　interpolation　algorithm,　the　asymmetrical　wavelets　constructed　based　on　data　fitting　are　more　suitable　in　feature　extraction　of　fault　signal　of　roller　bearings.