An all-fiber tunable laser was fabricated based on an acousto-optic tunable filter and a tapered fiber. The structure was of a high signal-to-noise ratio, therefore, no extra gain flattening was needed in the laser. In the experiment, the wavelength of the laser could be tuned from 1532.1 nm to 1570.4 nm with a 3-dB bandwidth of about 0.2 nm. Given enough nonlinearity in the laser cavity, it could also generate a sliding-frequency pulse train. The laser gains advantages of fast tuning and agility in pulse generation, and its simple structure is low cost for practical applications.