Abstract: In order to improve the distributed estimation performance of wireless sensor networks in non-Gaussian noise environment, a variable-scale diffusion adaptive filtering algorithm was proposed based on half-quadratic criterion in this paper, adopting a convex cost function half-quadratic criterion (HQC), The algorithm was designed to find an optimal solution more effectively, to get faster convergence speed and higher filtering accuracy, and possess stronger robustness to pulse noise. In addition, the variable scale factor was introduced to balance and further improve the convergence speed and steady-state error performance of the algorithm. Finally, the performance of the proposed algorithm was analyzed theoretically and compared in simulation. The results show that the proposed algorithm can provide higher identification efficiency for unknown systems under different non-Gaussian noise environments, and its convergence performance and steady-state error performance are better than other diffused adaptive filtering algorithms.