In order to improve the near-source region accuracy of the FFP (fast field program) of ocean acoustics, the factors affected the accuracy of the classical FFP were analyzed, which includes the approximation of Bessel function, the neglection of incoming wave term and the low sampling frequency at the farthest horizontal distance region. These factors can lead to large near-source region errors and incorrect results at the farthest horizontal distance region (after the calculation, the acoustic field in the region should be removed). Based on the classical FFP model, improving near-source region accuracy algorithms were presented, which includes the approximate Bessel function with incoming wave term and the solutions in the up-down two triangular domains by covering the source point and symmetric axis with the wavenumber integration solutions (using exact Bessel function). The test cases show that, compared with the classical FFP model, the proposed model can significantly improve the near-field calculation accuracy and the comprehensive performance under the condition of less absolute time increased; compared with the direct wavenumber integration method, the integration time of the improved model is significantly reduced and the practical application value is higher under the condition of the same error order of magnitude.