In this work, we compile a sample which contains 71 Gev Gamma-ray-loud Active Galactic Nuclei (AGNs) (14 BL Lacs and 57 FSRQs), 53 FR Ⅰ radio galaxies and 63 FR Ⅱ radio galaxies. We make a nonlinear least-square fit to this sample, and find that the best fit value of the Hubble constant is H0 =71 .5±3 .8 kms-1Mpc-1 with a reduced χ2 2 .46 by assuming Mv=-23 .0 and accepting q0=1 .0, and the corresponding regression line has a correlation index R≈0 .78. The best fit value of H0 =71 .5 ±3 .8 kms-1Mpc-1 is in well agreement with H0 =72 ±8 kms-1 obtained by the Hubble Space Telescope Key Project .Our results show that the Gev Gamma-ray emissions of AGNs can be used as cosmological standard candles indeed.
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