Thanks to an enormous release of light curves of contact binaries, it is a challenge to derive the parameters of contact binaries using the Phoebe program and the Wilson-Devinney program with the Markov chain Monte Carlo (MCMC) algorithm. In this paper, we use neural network (NN) and MCMC algorithm to derive the parameters of contact binaries. The fitting of models is still done with the MCMC algorithm, but that the neural network is used to establish the mapping relationship between the parameters and the light curves generated beforehand by Phoebe. The NN model is trained with a set of Phoebe-generated light curves with known input parameters, and then combined with the MCMC algorithm to quickly obtain the posterior distribution of the parameters. Two NN models without and with the influence of third light are established, which can generate light curves with 100 points faster than Phoebe by about four orders of magnitude under the same running condition. In addition, the two models can generate the light curves with an error of less than a millimagnitude. The feasibility of NN and MCMC algorithm is also verified by the synthetic light curves generated by Phoebe and the light curves from Kepler survey data. NN and MCMC algorithms can quickly derive the parameters and the corresponding parameter errors of contact binaries from sky survey. These parameters can also be used as more precise initial input values for the objectives of individual detailed studies.