In　order　to　solve　the　difficulty　of　compound　fault　diagnosis　of　rolling　bearings,　a　novel　rolling　bearings　fault　diagnosis　method　based　on　improved　tunable　Q-factor　wavelet　transform　(TQWT)　is　proposed　in　this　paper.　Firstly,　a　new　evaluation　index　of　signal　decomposition　called　KR　is　defined　by　summing　kurtosis　and　root　mean　square　(RMS)　with　weight.　KR　is　the　compromise　between　impulse　factor　and　energy　factor,　which　can　better　represent　the　fault　characteristics　of　sub-bands　obtained　by　TQWT.　Secondly,　the　KR　is　used　to　improve　the　TQWT.　The　improved　TQWT　can　adaptively　determine　the　parameters　Q-factor　and　decomposition　level.　Thirdly,　the　bearing　vibration　signal　is　decomposed　by　the　improved　TQWT　and　the　sub-bands　are　sorted　descending　according　to　the　KR.　Finally,　the　Hilbert　envelope　analysis　is　carried　out　and　the　fault　types　are　determined　by　comparing　the　fault　characteristic　frequencies　obtained　from　the　Hilbert　envelopes　to　the　fault　characteristic　frequencies　calculated　by　formula.　The　proposed　fault　diagnosis　method　is　fully　evaluated　by　simulation　and　experiments.　The　results　demonstrate　that　the　KR　takes　advantage　of　kurtosis　and　RMS　and　can　be　better　used　to　optimize　the　parameter　of　TQWT.　And　the　compound　fault　features　of　rolling　bearings　can　be　accurately　separated　into　different　sub-bands　by　the　improved　TQWT,　which　is　helpful　to　improve　the　accuracy　of　compound　fault　diagnosis　of　rolling　bearings.