In order to solve the problem that the traditional Gamma-distributed maximum a posteriori despeckling algorithm cannot effectively preserve the point target in the homogeneous region, nor effectively keep the weak edge, and nor efficiently suppress the speckle in the strong edge region, the Gamma-distributed maximum a posteriori despeckling algorithm with prior parameter estimation based on second-kind statistics is proposed for high-resolution synthetic aperture radar images. Using the Mellin convolution and the multiplicative model of speckle, the parameters of the Gamma prior distribution are accurately estimated from the first two log-cumulants of the observed image. The proposed algorithm has the analytical filtering output, and it is easy to implement. Despeckling experiments on high-resolution synthetic aperture radar images of agricultural field and urban region demonstrate that compared with the traditional Gamma-distributed maximum a posteriori despeckling algorithm, the proposed one can effectively preserve the point target in the homogenous region, effectively retain the weak edge, and efficiently suppress the speckle in the strong edge region.