Analytic image technique and wavelet transform(WT) technique are applied to analysis of interferometry hologram with a linear carrier. In this method, Hilbert transform is firstly performed on the hologram to get the analytic signals. And then WT is calculated on the signal. Finally, the phase information of the hologram can be obtained from the WT coefficients at the wavelet ridge position. Because of the good spatial localization ability of the mother wavelet, the error caused by the boundary of the hologram is limited in local areas. Filtering process is avoided in this method, so it can resolve the frequency overlapping problem to a certain extent. Mathematical demonstration is given in detail. Computer simulation and experiments verify the validity of the proposed method.