A rapid and precise algorithm without phase unwrapping for phase retrieval from a single carrier-frequency fringe pattern is proposed. The algorithm first gains sinusoidal component and cosine component of the fringe pattern by Hilbert transform twice,and then phase is retrieved by the line integral of its gradient calculated by the sinusoidal and cosine components. The performance of the proposed method is evaluated by computer simulation and experiment. The phase error from phase unwrapped by Fourier transform is avoided. The algorithm is simple and insensitive to the shadow and discontinuous region.