We report a novel scheme for a fiber-optic hydrogen sensor based on an erbium-doped fiber laser with a palladium-coated tapered fiber within the laser cavity. The tapered fiber acts as a hydrogen-sensing element. When the sensing element is exposed to a hydrogen atmosphere, its attenuation decreases, changing the cavity losses and leading to a modification of the laser transient. The hydrogen concentration is obtained by simple measurement of the buildup time of the laser. This technique translates the measurement of hydrogen concentration into the time domain, and it can be extended to many intensity-based fiber sensors. Relative variations in the buildup time of up to 55% at an increase of the hydrogen concentration from 0 to 10% are achieved with a resolution of better than 0.1%.