We describe a simple, narrow-linewidth, tunable fiber-based laser with a high degree of tuning accuracy. A polarization independent semiconductor optical amplifier (SOA) is used as the gain medium in a unidirectional fiber ring cavity with a circulator connected to a 6-meter long chirped fiber Bragg grating (CFBG). The laser wavelength is chosen by setting the modulation frequency of the SOA the same as the harmonics of the fundamental repetition rate of the light reflected at a specific point on the CFBG. Careful management of the drive current and pulse width helps to generate laser light of narrow linewidth (less than 0.03 nm) with low power variation (1.46 dB) over a tuning range of 40 nm.