Metamaterials and metasurfaces show great potentials to adjust the amplitude, phase, wavefront and direction of electromagnetic waves in a complex and precise manner, since the shape and size of the subwavelength unit can be designed with large degree of freedom. At the same time, with the increase of the number of structural parameters involved, the structural design time increases in an exponential way. This paper proposes a method for the fast optimization of metasurface structures based on the back-propagation (BP) neural network, and a terahertz dielectric metagrating with the merits of high diffraction efficiency, wide bandwidth, and high angular dispersion is achieved. A dataset established via a limited number of rigorous coupled wave analyses is used to train the BP neural network. It can accurately predict the diffraction spectrum of the metagrating with an arbitrary geometry. Simultaneously, the metagrating with the highest diffraction efficiency and wide bandwidth is fast selected by quickly traversing all structural parameters. The designed speed is increased by 10,000 times compared with that of the traditional traversing calculation method, which proves the high efficiency and accuracy of the metasurface optimization method based on the BP neural network. The study provides a diffractive element with excellent performance for terahertz applications.