This communication addresses the issue of nonlinear filtering for non-Gaussian systems. A two-stage distributed diffusion maximum correntropy CKF algorithm is devised, which includes local estimation and diffusion fusion. In the local estimation stage, the node exchanges predicted estimates with its neighboring nodes to yield a consensus term for enhancing the local estimate. To avoid the computation of cross-covariances, a rational upper bound (UB) of covariance is constructed, the gain matrix and local estimator are deduced according to the maximum correntropy (MC) rule. In the diffusion fusion stage, the node further exchanges local estimates with neighboring nodes and fuses them by covariance intersection technique and diffusion fusion strategy, which avoids the correlation information and the transmission of raw measurement information. It combines the merits of both consensus estimator and diffusion estimator. The cubature rule and statistical linearization approach are employed in the proposed algorithm, which does not involve Jacobi matrices thereby is more accurate and stable. And it is proved to be converged. Finally, the simulation experiment confirms the superiority and effectiveness of the approach.