In order to improve the computational stability and accuracy of the acoustic wavenumber integration propagator matrix approach, the automatic selection algorithm for maximum truncate wavenumber based on predictor-corrector theory was proposed. The algorithm has the advantages of simple, reliable and small computational load. The test results of acoustic spherical wave in free space show that the stability of propagator with the order of bottom to top is relatively poor, the non-physical divergence of the wavenumber kernel function is easy to appear above the sound source, so it was necessary to use different truncate wavenumbers at different depths to calculate the correct result; while the calculation stability and precision of propagator with the order of bottom to source and top to source respectively reach higher levels.