A recording method to suppress the zero-order diffraction term in an off-axial digital hologram and to improve its effective bandwidth is proposed. The method records the hologram on the condition that the reference intensity is more stronger than that of the object. Then, the recorded hologram is normalized by the recorded reference intensity beforehand. The natural logarithm operation and Hilbert transform are applied to the normal hologram to suppress the zero-order diffraction and the object complex field is recovered by an exponential operation. The theory of the method is analyzed. It shows that the logarithm operation can suppress the zero-order term and the Hilbert transform can filter the desired term. Finally, the experiments are performed to validate the method. The results show that the method can suppress the zero-order diffraction term efficiently even in the case of the strong spectral overlap between the zero-order term and the diffraction orders. The influence of the intensity ratio of the light of reference to that of object on the suppression efficient of zero-order diffraction term is analyzed. It shows that the zero-order term can be efficiently suppressed through the proposed method when the intensity ratio is above 5.