We report the optical identifications of two X-ray luminous point sources in the spiral galaxy NGC 4565 based on archive data of Chandra and the Hubble Space Telescope . The central X-ray point source , RXJ1236.3+2559 , is found to be the nucleus of NGC 4565 with an X-ray luminosity of L _ { x } \approx 4.3 \times 10 ^ { 39 } erg s ^ { -1 } . We show that its multi-waveband properties are consistent with it being a low-luminosity active galactic nucleus . A faint optical counterpart with B \approx 25.1 and I \approx 24.0 was identified for the off-nucleus X-ray point source , RXJ1236.2+2558 . Its extinction-corrected B magnitude is estimated to be 24.5 . The X-ray to optical flux ratio ( f _ { X } / f _ { B } ) is about 540 . From the optical and X-ray properties we argue that RXJ1236.2+2558 is an ultra-luminous X-ray compact source with L _ { x } \approx 6.5 \times 10 ^ { 39 } erg s ^ { -1 } . The source is probably located in a faint globular cluster at the outer edge of NGC 4565 ’ s bulge .