Fiber-fed etalons are widely employed in advanced interferometric instruments such as gravitational-wave detectors, ultrastable lasers and calibration reference for high-precision spectrographs. We demonstrate that variation in near-field distribution of the feeding fiber would deteriorate the spectrum precision of the fiber-fed Fabry-Perot etalon, especially when precision at the order of 3 x 10(-10) or higher is required. The octagonal fiber reinforced with double scrambler could greatly improve the steadiness and uniformness of the near-field distribution. When building wavelength calibrators for sub-m s(-1) precision radial-velocity instruments, the double scrambler should be considered meticulously.