We demonstrate a dispersion-tuned fiber optical parametric oscillator (FOPO)-based swept source with a sweep rate of 40 kHz and a wavelength tuning range of 109 nm around 1550 nm. The cumulative speed exceeds 4,000,000 nm/s. The FOPO is pumped by a sinusoidally modulated pump, which is driven by a clock sweeping linearly from 1 to 1.0006 GHz. A spool of dispersion-compensating fiber is added inside the cavity to perform dispersion tuning. The instantaneous linewidth is 0.8 nm without the use of any wavelength selective element inside the cavity. 1 GHz pulses with pulse width of 150 ps are generated.