The　selection　of　optimal　frequency　band　sensitive　to　fault　is　significant　for　bearing　fault　diagnosis.　However,　prior　knowledge　of　fault　characteristic　frequency　is　usually　essential　in　this　operation.　To　address　this　issue,　an　optimal　candidate　fault　frequency　periodicity　index　optimization-gram　is　proposed.　First,　the　spectral　coherence　theory　is　exploited　to　transform　the　vibration　signal　into　a　two-dimensional　map　consisting　of　cyclic　and　spectral　frequencies.　Second,　a　novel　optimal　candidate　fault　frequency　periodicity　index　is　constructed　based　on　optimal　candidate　fault　frequencies,　which　fully　excavates　the　fault　information　hidden　in　a　two-dimensional　plane　by　utilizing　modulation　characteristics　of　bearing　fault　signal　and　transforms　it　into　a　specific　numerical　series.　Then,　the　optimal　candidate　fault　frequency　periodicity　index　optimization-gram　is　further　developed　to　identify　the　optimal　frequency　band,　where　the　optimal　candidate　fault　frequency　periodicity　index　is　utilized　to　quantify　the　fault　information　in　the　frequency　bands　separated　by　1/3-binary　tree　filter　bank.　Finally,　an　improved　envelope　spectrum　is　obtained　by　integrating　the　spectral　coherence　over　the　optimal　frequency　band.　The　optimal　candidate　fault　frequency　periodicity　index　optimization-gram　is　demonstrated　by　simulated　and　experimental　signals,　and　the　results　demonstrate　that　it　is　superior　to　other　methods.