Abstract: Based on the near-field acoustic holography theory of equivalent source method, the equivalent source strength and the integral kernel function perform a bidirectional Fourier series expansion on the axisymmetric virtual plane, so that the unknown source strength vector is transformed into a sparse Fourier expansion coefficient vector. Combined with the basis pursuit de-noising algorithm in the compressed sensing reconstruction algorithm, a semianalytical and semi-numerical equivalent source near-field acoustic holography method is established based on the compressed sensing and fast wave superposition spectral method. The pulsating spherical sound source and the long-strip sound source are taken as the numerical examples to compare the sound field reconstruction effects. The results show that the reconstruction accuracy of the proposed method is the same as the traditional method at the low frequency, but its reconstruction accuracy and anti-noise performance are better than the traditional method with the increase of frequency.