Based on the fast convergent Fourier model,the transmittance of the graphene gratings was calculated in terahertz waveband,the influences of Fermi energy,grating period,grating duty cycle and relaxation time of the graphene gratings on the transmittance were discussed under two conditions of normal incidence and fixed frequency.The results show that when the incident TM polarized plane wave is normal to the graphene gratings,the transmittance decreases to a minimum and then increases with the increase of frequency,and the minimum value of transmittance is smaller when the values of Fermi energy,grating duty cycle and relaxation time are bigger.The transmittance increases to a maximum and then decreases with the increase of incident angle when the incident frequency is fixed.Meanwhile,the transmittance gains the maximum value while the incident angle is about 60 degrees.The results of this study will provide significant guidance for the study of graphene gratings.