The phase noise of the f-to-2f interferometer used for stabilizing the carrier-envelope phase of a femtosecond laser oscillator was studied by adding a He-Ne laser beam co-propagating with the short pulse laser beam. The noise was reduced to ~60 mrad by stabilizing the optical path length difference of the interferometer. This suppressed the fast jitter of the carrier-envelope phase of the amplified laser pulses from 79 to 48 mrad.