We examine the effects of transmission error on the digital holograms in phase-shifting digital holography. It is evident that the reconstruction object image is vulnerable to transmission errors from the noise channel. An estimation-based reconstruction algorithm is used to detect the error points and the largest-error hologram of the error points. Based on the detection result, the adaptive algorithm reconstructs the digital hologram by removing the noise effect on the largest-error hologram. With accurate detection, the proposed algorithm is able to reconstruct an object image from a digital hologram with severe transmission errors.