Aiming at the periodic boundary problem of phase detection in the existing turbulent random phase difference demodulation algorithms in optical fiber turbulence measurement technology, an atmospheric optical turbulent phase difference demodulation algorithm combined with phase unwrapping technology, called Phase Generated Carrier Unwrapping (PGCU), is proposed in this work based on the principle of internal modulation phase carrier technology and its signal expression. Through numerical simulation, the demodulation errors of the algorithm and the traditional Differential Cross Multiplication (DCM) algorithm under different conditions were compared and analyzed. The simulation results show that the PGCU algorithm can not only break through the periodic boundary of the detection phase, but also significantly reduce the average demodulation error by 7～11 orders of magnitude compared to the DCM algorithm under the condition of turbulence changing from strong to weak. Besides, the demodulation error has a positive correlation with the signal amplitude and frequency. And when the modulation frequency is increased from 2000 Hz to 7000 Hz, the maximum demodulation error of PGCU algorithm is reduced by 4 orders of magnitude, while that of DCM algorithm can only be reduced by 8.8%. In addition, a dynamic tracking modulation frequency algorithm is also proposed to solve the error problem caused by modulation frequency fluctuation. Finally, through the experiment of demodulating the phase difference generated by piezoelectric ceramics, it is found that the minimum relative error between the demodulated phase and the measured phase is 1.18% and the maximum relative error is 11.61%, which preliminarily verifies the reliability and accuracy of the PGCU algorithm. By introducing phase solution wrapping technology, this study has improved the detection range of turbulent random phase difference and greatly reduced the demodulation error, which provides important guidance for the practical application of fiber turbulence measurement systems.