We report supercontinuum generation by launching femtosecond Yb fiber laser pulses into a tapered single-mode fiber of 3 um core diameter. A spectrum of more than one octave, from 550 to 1400 nm, has been obtained with an output power of 1.3 W at a repetition rate of 250 MHz, corresponding to a coupling efficiency of up to 60%. By using a typical f-2f interferometer, the carrier envelope offset frequency was measured and found to have a signal-to-noise ratio of nearly 30 dB.