For the problem of the restoration of the infrared turbulence-degraded image with complex background,the items of some anisotropic weighted differences are constructed mainly in this paper.The minimization of 2-norm of the second-order differences to be functioned as a spatial correction constraint is incorporated in the estimation process of solving for the values of the point spread functions.A restoration algorithm for two neighboring frames of turbulence-degraded images with complex background is proposed.Series of experiment and comparing results show that the proposed algorithm is effective for the restoration of infrared turbulence-degraded image with complex background.