Traditional Nakagami fading models can not provide satisfactory temporal correlation. Based on channel decomposition technique and sum-of-sinusoids (SOS) method, a novel complex Nakagami fading channel simulator was proposed. The new model allows for arbitrary fading parameter and prespecified temporal correlation. In this paper, we firstly derived the relationships between Rayleigh and Nakagami random process, and then presented a modified Nakagami envelope decomposition model by Rayleigh processes. Finally, arbitrary temporal correlated Nakagami fadings are generated combining with SOS method. Simulation results verify that the output channel of new model has more accurate autocorrelation coefficient than other models, and the statistical properties, such as envelope and phase distributions, are also very close to the theoretical results