Geometric optimization of piccolo tube provides a cost-effective approach to shorten the design circle of hot-air anti-icing system and maximize the utilization efficiency of bleed air. An optimization methodology for aircraft hot-air anti-icing systems based on Reduced Order Method (ROM) is developed. ROM based on Proper Orthogonal Decomposition (POD) and Radial Basis Function neural network (RBF) is constructed to evaluate objective and constraint functions of single- and multi-objective optimizations. POD is adopted for data compression and characteristics extraction for the anti-icing performance snapshot matrix. Then, a lower-dimensional approximation for the snapshot matrix is derived from the projection subspace consisting of a set of basis modes. RBF neural network is introduced to construct the mapping between the design variables of piccolo tube geometric configuration samples and the linear combination coefficients of basis modes. The piccolo tube is parameterized by five design variables and is optimized by the developed methodology. The predicted results indicate that the constructed ROM can provide the distributions of surface temperature and runback water with high accuracy and computational efficiency. The optimal results indicate that the developed optimization methodology is efficient and reliable for handling single- and multi-objective design problems of aircraft piccolo tube hot-air anti-icing systems.