The temporal characteristics of the free space optical communication (FSOC) turbulence fading channel are essential for analyzing the bit error rate (BER) performances and compiling the rationale of adaptive signal processing algorithms. However, the investigation is still limited since the majority of temporal sequence generation fails to combine the autocorrelation function (ACF) of the FSOC system parameters, and using the simplified formula results in the loss of detailed information for turbulence disturbances. In this paper, considering the ACF of engineering measurable atmospheric parameters, we propose a continuous-time FSOC channel fading sequence generation model that obeys the Gamma-Gamma (G-G) probability density function (PDF). First, under the influence of parameters such as transmission distance, optical wavelength, scintillation index, and atmospheric structural constant, the normalized channel fading models of ACF and PSD are established, and the numerical solution of the time-domain Gaussian correlation sequence is derived. Moreover, the light intensity generation model obeying the time-domain correlation with statistical distribution information is derived after employing the rank mapping, taking into account the association between the G-G PDF parameters and the large and small scales turbulence fading channels. Finally, the Monte Carlo numerical method is used to analyze the performances of the ACF, PDF, and PSD parameters, as well as the temporal characteristics of the generated sequence, and the matching relationships between these parameters and theory, under various turbulence intensities, propagation distances, and transverse wind speeds. Numerical results show that the proposed temporal sequence generation model highly restores the disturbance information in different frequency bands for the turbulence fading channels, and the agreement with the theoretical solution is 0.999. This study presents essential numerical simulation methods for analyzing and evaluating the temporal properties of modulated signals. When sophisticated algorithms are used to handle FSOC signals, our proposed temporal sequence model can provide communication signal experimental sample data generating techniques under various FSOC parameters, which is a crucial theoretical basis for evaluating algorithm performances.