Abstract: The high-fidelity sonic-boom prediction is crucial for the design of low-boom supersonic transport aircraft. In this article, a far-field sonic-boom prediction method solving the augmented Burgers equation is studied, and a prediction code called "bBoom" is developed. First, the numerical method for solving augmented Burgers equation and a ray tracing method in propagation are studied. Some significant parameters of molecular relaxation processes and thermoviscous absorption in the Burgers equation are presented. Second, some benchmark cases from the 2^th AIAA Sonic Boom Prediction Workshop, including a simple axi-symmetric body, a NASA low-boom configuration, and LM1021 configuration, are employed to validate the code. The results show that the developed code is accurate and reliable for predicting the far-field waveforms. At last, far-field sonic boom waveforms propagated from different near-field pressure signals at different locations are compared, and the distinction of waveforms in different flight azimuthal angles with atmospheric winds is investigated. It is shown that, in order to improve the accuracy of predicting the sonic boom for configurations like a C25D model, the near-field signal should be extracted at a distance of three body lengths off the aircraft. It is also shown that atmospheric wind profiles have a significant impact on the sonic-boom waveform and sonic-boom carpet on the ground.