A digital reconstruction method of Fresnel hologram with a ridge of Gabor wavelet transform is described. Applied the Gabor wavelet transform to the digital holography, the object wave can be numerical reconstructed without the spatial filtering. The Gabor wavelet transform and the ridge of the wavelet transform are introduced. It proves that by abstracting the wavelet coefficients at the ridge of the wavelet transform of the hologram, the intensity and the phase of the object wave corresponding to the +1-order spectrum at the hologram plane are obtained, at the same time the effect of the zero-order diffraction image and the twin image is eliminated. Multiplying the wavelet coefficients at the ridge by an ideal wave corresponding to a replica of the reference wave and propagating for the corresponding propagation distance, the reconstructed wave at the image plane is reconstructed, and a clear image is obtained. The results of a simulated phase object and an experiment show that the method is effective.