Understanding the complicated kinetic process involved in nanoparticle self-assembly is of considerable importance for designing and fabricating functional nanostructures with desired properties. In this work, using the stopped-flow absorption technique, we investigate kinetic behaviors involved in gold nanorod assembly mediated by cysteine molecules. Further combining with SEM microstructural analyses of the assembly structure of gold nanorods, we establish the correlations between the kinetic parameter and the assembled structure. The dynamical surface plasmonic absorptions of gold nanorods are monitored during the formation of GNRs chains with different assembly rates. And the acquired kinetic data are analyzed in the frame of the second-order theoretical model, which has been widely used in the literature for linear assembly of gold nanorods. We find that the second-order theoretical model for describing the kinetic behaviors is merely limited to the case of slow assembly process of gold nanorods, but shows large deviation when the assembly process is relatively fast. We, therefore, propose in this work a new kinetic model on the basis of the logistic function, to make kinetic analyses for the different assembly rates of gold nanorods. Compared with the second-order theoretical model, this new logistic function model possesses an extended validity in describing the kinetic behaviors of both the slow and relatively fast nanorods assembly. Particularly, due to introduction of a new parameter, i.e., the exponential parameter p, the logistic function model enables a more accurate description of the kinetic behavior at a very earlier assembly stage (e.g., on a millisecond scale), in addition to quantifying the assembly rate T0. More importantly, the value of p derived from the new logistic function model allows us to establish the kinetics-structure relationship. The slow assembly process that produces mainly the one-dimensional linear chains of nanorods, is featured by the value of kinetic parameter p close to 1. By contrast, for the relatively fast assembly process that results in the formations of irregular zigzag chains even two-dimensional assembled structures of nanorods, the value of kinetic parameter approaches to 2. Furthermore, in the present study, the kinetic parameter p based on the logistic model might be related to the fractal dimension (Df) of the aggregated structures of the gold nanorods self-assembly processes. These results suggest that the logistic function model could provide the kinetic features for directly quantifying the fractal structures of the nanorods assembly. We believe that the new kinetic analysis method presented in this work could be helpful for an in-depth understanding of the kinetics-structure-property relationship in self-assembled plasmonic nanostructures.