CW all-fiber optical parametric oscillator (FOPO) with tuning range from 950 to 1010 nm is demonstrated using birefringent photonic crystal fiber pumped by an Ytterbium-doped fiber laser (YDFL) near 1 μm. CW parametric generation with spectral linewidth of 3.7 nm at 972 nm has been obtained with slope efficiency as high as 9.4% and output power of up to 460 mW. It is also shown that the FOPO slope efficiency reaches 25% after narrowing of the pump spectrum down to 40 pm. At that the generated power exceeds 1 W, but in this case the generated radiation is modulated with 48 ns period and 50% duty factor due to pump laser power modulation which is probably caused by stimulated Brillouin back scattering.