Quantum nonlocality, as an invaluable quantum resource, plays an indispensable role in processing numerous quantum information. Accurate characterization and effective detection of nonlocality have always been important and challenging topics in theoretical and experimental quantum information research. How to precisely identify and verify the phenomenon of quantum nonlocality in complex many-body quantum systems, and how to design more efficient detection methods for the nonlocality, have become urgent scientific issues that need to be addressed. This paper is dedicated to the detection of multipartite quantum nonlocality, with a focus on exploring how the Svetlichny inequality can be used to detect it. First, the maximum quantum violation of the Svetlichny inequality is discussed. Through construction, a quantum state \rho_0 and a set of observables \mathscrA_0 are obtained, thereby achieving the maximum quantum violation of the Svetlichny inequality. It is also demonstrated how to construct other quantum states and sets of observables to achieve their maximum violation of the Svetlichny inequality, thereby clarifying that the quantum states and sets of observables that achieve the maximum quantum violation of the Svetlichny inequality are not unique. Second, in order to find more quantum states and sets of observables that violate the Svetlichny inequality, a corresponding Hamiltonian is constructed using the Svetlichny operator. This core issue of finding quantum states that violate the Svetlichny inequality is ingeniously transformed into solving the ground state of this Hamiltonian. Leveraging the powerful function approximation capability of neural networks, neural network quantum states are constructed. Two optimization algorithms, i.e. the Nelder-Mead simplex method and quantum variational Monte Carlo (VMC), are respectively adopted to optimize the network parameters in order to find the ground state energy and ground state of the Hamiltonian, thereby achieving a violation of the Svetlichny inequality and ultimately detecting nonlocal states. To ensure the efficiency and accuracy of the detection method, we conduct a comparative study of different optimization methods. By comparing the Nelder-Mead simplex method with the VMC method, we find that the VMC method is more suitable for nonlocality detection based on neural network quantum states in terms of efficiency and accuracy, providing reliable computational support for detecting many-body quantum nonlocality and the violation of the Svetlichny inequality. To verify the validity and universality of the proposed method, we detect the nonlocality of multipartite quantum pure states by using neural network quantum states and the VMC method under different Hamiltonians. The results indicate that this method successfully captures violations of the Svetlichny inequality in many-body quantum systems, thereby achieving effective detection of multipartite quantum nonlocality. This fully confirms the validity and universal potential of the VMC method in nonlocality detection based on neural network quantum states. This study not only verifies the theoretical and technical feasibility of detecting multipartite quantum nonlocality based on neural network quantum states and the VMC method, but also provides valuable new insights for detecting nonlocality. More importantly, it opens up a new research avenue for using neural networks to solve complex quantum many-body problems.