The DAMAS algorithm has high spatial resolution. But, the unsatisfactory dynamic range leads to false acoustic sources in the imaging results. The F-DAMAS algorithm is proposed to solve this problem, which exploits the functional beamforming ( FB) algorithm to improve the imaging performance. By powering the PSF in the DAMAS algorithm, the linear relationship among the output power of the FB algorithm, the powered PSF and the acoustic source distribution is established. And the equation group of the F-DAMAS is formed. Furthermore, the Gauss-Seidel iterative method with positive constraints is utilized to derive the acoustic source distribution. Compared with FB and DAMAS algorithms, simulations and experiments on mono and incoherent acoustic sources show that the proposed algorithm can effectively improve resolution and dynamic performance of the image. According to the relationship between the coverage area of the acoustic center and the change of the power index, it recommends that the value range of the power index in the algorithm is 6 ~ 14.