We have studied the luminosity-timescales relation 0f29 γ-ray-loud blazars with observed minimum variation timescales. Following the acceleration model of Ghisellini and Maraschi (1989 Astrophys. J. 340 189), a relation between the variation of the timescale in γ-rays and that in other wavebands has been derived. Both the observed and Doppler-corrected γ-ray luminosity-time scales relations have been calculated. The observed luminosity of the majority of sources is above the Eddington limit. The intrinsic luminosity of all sources is below the Eddington limit, suggesting that the γ-ray emission of the γ-ray-loud blazar originates from relativistic jets.