The researches on the alternating direction method of multipliers (ADMM) for solving two-block optimization have been gradually perfect. However, the studies on ADMM for solving nonconvex multi-block optimization are relatively few. In this paper, we propose a symmetric proximal ADMM with relaxation stepsize parameter for nonconvex multi-block optimization. Under some suitable conditions, the global convergence of the algorithm is established. Subsequently, the strong convergence of the algorithm is established when the benefit function satisfies the Kurdyka-{\L}ojasiewicz (KL) property. Finally, numerical experiments verify the effectiveness of the proposed method.