This paper demonstrates the application of a coupled Computational Fluid Dynamics and Computational Aeroacoustics based Kriging-based optimization technique to the aeroacoustics design of an aero-engine bypass duct. In this paper, full influence of non-uniform background flows through the duct and the shear layer on sound propagation and radiation is included in the computations. The noise prediction system using 2.5D APE model is verified with a canonical case of sound propagation out of a semi-infinite duct with flow. Excellent result is obtained for the verification problem. Numerical analysis of noise radiation from a general turbofan bypass duct is then carried out. The mean flow is obtained from Reynolds Averaged Navier-Stokes solutions using the Fluent solver. The numerical difficulties present with the sheared flows in ducts are overcome by solving the 2.5DAPE equations using a linearized Euler solver in time domain. In particular, the noise reduction by a geometry optimization concept is investigated. With the optimization system based on Gaussian process-based Kriging and a genetic algorithm, an axi-symmetric bypass duct is optimized successfully and effectively by using the geometry optimization procedures. Results from the optimum bypass geometry are presented, and show that 2.5 dB noise reductions can be achieved. The results show that the optimization can effectively change the noise level and the directivity pattern in the far field.