The light scattering of multilayer nanoparticles can be solved by Maxwell equations. However, it is difficult to solve the inverse design of multilayer nanoparticles by using the traditional trial-and-error method. Here, we present a method for forward simulation and inverse design of multilayer nanoparticles. We combine the global search ability of genetic algorithm with the local search ability of neural network. First, the genetic algorithm is used to find a suitable solution, and then the neural network is used to fine-tune it. Due to the non-unique relationship between physical structures and optical responses, we first train a forward neural network, and then it is applied to the inverse design of multilayer nanoparticles. Not only here, this method can easily be extended to predict and find the best design parameters for other optical structures.