In this talk, we will introduce a parametric representation-oriented neural network (PRNN-STO) method to efficiently solve shape and topology optimization problems for complex geometries. This is a mesh-free optimization method that integrates the alternating direction method of multipliers (ADMM) with a deep neural network solver. In addition, a low-dimensional parameterized representation is used to construct a continuous design space, which enables a global, explicit and smooth description of the structural topology. Some numerical examples are given to demonstrate the accuracy, robustness, and effectiveness of the PRNN-STO method in solving shape and topology optimization problems.