It is complicated to model the acoustic field in stratified ocean for airborne aircraft, due to high speed of the source and air-to-water sound transmission. To our knowledge, there are very few papers in the open literature dealing with this complicated problem; but, in our opinion,they all require great amount of computation. We now propose a different method that requires much less computation. We improve the wavenumber integration method to model the received temporal signal for a moving source in stratified ocean and sum up in a concise form the core of our paper as follows: (A) Eq. (11) can be calculated by means of fast Chirp Z transform and the signals at all N time points are generated simultaneously; (B) direct numerical evaluation of the wavenumber integral in Eq. (4) produces large numerical errors; so it is necessary to shift the integration slightly below the real axis; (C) we compare the computation cost of direct calculation method with that of our fast calculation method ; from the results presented in table 1,we can see that the fast calculation method consumes much less computation time, particularly for long duration signals; (D) for an airborne rapidly moving source, we compute the Dopplershifted signals in shallow water and analyze their short-time Fourier transform; from Fig. 1b, we can see that the received signals have multiple frequency components for a tonal source due to source motion and that each component corresponds to an arrival path.