This paper proposes a digital holographic phase demodulation approach based on the transport intensity equation (TIE), which is solved with a discrete cosine transform. Simulative and experimental findings reveal that the new approach successfully accelerates the unwrapping process with no loss of accuracy compared with the traditional approach based on fast Fourier transform. The new approaches' efficiency can still be enhanced after choosing a suitable extending scheme for the computation of the axis derivative of intensity. The proposed new TIE-based phase unwrapping approaches can lead to the real-time uses of the phase measurement with high processing speed and precision.