With the continuous development of large optical surveys, a large number of light curves of late-type contact binary systems (CBs) have been released. Deriving parameters for CBs using the the Wilson-Devinney program and the PHOEBE program poses a challenge. Therefore, this study developed a method for rapidly deriving light curves based on the Neural Networks model combined with the Hamiltonian Monte Carlo (HMC) algorithm (NNHMC). The neural network was employed to establish the mapping relationship between the parameters and the pregenerated light curves by the PHOEBE program, and the HMC algorithm was used to obtain the posterior distribution of the parameters. The NNHMC method was applied to a large contact binary sample from the Catalina Sky Survey, and a total of 19104 late-type contact binary parameters were derived. Among them, 5172 have an inclination greater than 70{deg} and a temperature difference less than 400K. The obtained results were compared with the previous studies for 30 CBs, and there was an essentially consistent goodness- of-fit (R2) distribution between them. The NNHMC method possesses the capability to simultaneously derive parameters for a vast number of targets. Furthermore, it can provide an extremely efficient tool for the rapid derivation of parameters in future sky surveys involving large samples of CBs.