An all- fiber 30 kHz repetition rate swept laser source at a center wavelength of 1340 nm with narrow instantaneous linewidth is built for swept source optical coherence tomography. The phase and the intensity of the swept source are stable. The scanning range of the swept source is 10 nm, the full width at half maximum is 6 nm, the instantaneous linewidth is less than 0.018 nm and the average output power is 9.1 mW. Based on the Fourier-domain mode locking, the swept laser source uses a Fabry-Perot interferometer tunable filter (FFP- TF) with finesse of 5578 and narrow transmission window. Spontaneous emission of the gain medium is used as background light, and passes through the long dispersion managed delay line into the FFPTF. After filtering and parameter matching, the system can resonate and produce an ultra- stable swept laser. The factors influencing the instantaneous linewidth of the swept source are discussed. The swept laser source shows high finesse which makes it suitable for high- speed molecular spectroscopy and molecular absorption spectroscopy.