It is complicated to model the acoustic field in stratified ocean for airborne aircraft, due to high speed of the source and acoustic transmission across the air-water interface. The wavenumber integration representation given by Schmidt and Kuperman can be used to model the temporal received signal for a moving source in stratified media. However, it requires intensive computation for calculating two-dimensional integrals at each time sampling point. In this paper, a faster calculation method is presented, and the computation cost for the integrals can be reduced obviously. The acoustic fields in both shallow water and deep-sea environments were computed using this method with rapidly moving airborne source. When the source moves through a static receiver, an approximation of one-dimensional wave-number integration can be obtained by stationary phase method.