Abstract: This paper describes an algorithm of numerical reconstruction for coaxial digital holography by means of a single phase-shift. In this algorithm, the intensity of the reference wave, the intensity of the object wave and their interference intensity are recorded respectively, and the object wave is calculated from these three intensity frames, but the object phase is ambiguous. Then a phase-shift frame corrects the object phase. Compared with the other single phase-shift algorithm, the phase-shift frame in this algorithm is not joins in the calculations of the object wave, but makes it without ambiguity. So, the algorithm is not sensitive to the phase-shifted error.