In modern radar systems, the Generalized compound distribution model is more suitable for describing the amplitude distribution characteristics of radar sea clutter. Accurately and efficiently simulating sea clutter has important practical significance for radar signal processing and sea surface target detection. However, in traditional zero memory nonlinearity (ZMNL) method, the correlated Generalized compound distribution model cannot deal with non-integral or non-semi-integral parameter. In order to overcome this shortcoming, a new method of generating correlated Generalized compound distributed clutter is proposed, which changes the generation method of Generalized Gamma distributed random sequences in traditional Generalized compound distribution models. Firstly, by combining with the Gamma distribution and using the additivity of the Gamma distribution, the Probability Density Function (PDF) of Gamma function is transformed into a second-order nonlinear ordinary differential equation, and the Gamma distributed sequence under arbitrary parameter is solved. Then the Generalized Gamma distributed sequence with arbitrary parameter can be obtained through the nonlinear transformation relationship between the Generalized Gamma distribution and the Gamma distribution, so that the shape parameters of the Generalized compound distributed sea clutter are extended to general real numbers. Simulation results show that the proposed method is not only suitable for clutter simulation with non-integral or non-semi-integral shape parameter values, but also further improves the fitting degree.