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We investigate the noise properties of a femtosecond all-fiber Cherenkov radiation source with emission wavelength 600 nm, based on an Yb-fiber laser and a highly nonlinear photonic crystal fiber. A relative intensity noise as low as 103 dBc/Hz, corresponding to 2.48% pulse-to-pulse fluctuation in energy, is observed at the Cherenkov radiation output power of 4.3 mW, or 150 pJ-pulse energy. This pulse-to-pulse fluctuation is at least 10.6-dB lower compared to spectrally sliced supercontinuum sources traditionally used for ultrafast fiber-based generation at visible wavelengths. Low noise makes all-fiber Cherenkov sources promising for biophotonics applications such as multiphoton microscopy, where minimum pulse-to-pulse energy fluctuation is required. We present the dependency of the noise figure on both the Cherenkov radiation output power and its spectrum.