Passively mode-locked fiber lasers are the best pulsed sources available today due to their simplicity and their ability to generate transform-limited pulses in the picosecond regimes. A drawback of the conventional passively mode-locked fiber lasers is that the pulse repetition rate is relatively low, at best a few tens of MHz, because of long cavity length. In order to raise repetition rate up to a few GHz, the cavity length has to be shortened below a few centimeters. Fiber lasers with such a short cavity require a high gain fiber and a small saturable absorber with low loss. Recently, the authors have proposed and demonstrated a small and low-loss saturable absorber device incorporating carbon nanotubes (CNT). Using CNT, we have realized very stable 2cm-long, 5GHz mode-locked Er:Yb-codoped silica-fiber laser, but the output power was limited to ∼0.2mW due to insufficient gain in the Er:Yb-codoped silica-fiber. Here we used heavily Er:Yb-codoped phosphate fiber to form 1 cm-long cavity with fiber mirrors, and succeeded in generating stable pulse trains with output power as high as 30mW and repetition rate as high as 10GHz at 1535nm.