Abstract: In order to calculate the acoustic radiation from frequency band vibrating bodies in half space, we propose the improved half-space FAQP(Frequency Averaged Quadratic Pressure) method based on energy sources to calculate the pressure radiated from frequency band vibrating bodies and obtain a unique solution for radiation at irregular frequencies. Numerical results of a pulsating sphere under a rigid surface and a pulsating hemisphere sitting on a free surface with bandwidth Δf=4 Hz show that the validity of the improved half-space FAQP method for solving the non-uniqueness problem is verified. And numerical results of a pulsating sphere under a rigid surface and a pulsating hemisphere sitting on a free surface show that, compared with the conventional BEM, improved half-space FAQP method can have much higher accuracy and is more suitable for high frequency calculation.