To tackle the staircase effect pro blem of classical total variational models(TV) in SAR image d enoising, a high order variational model based on Euler′s elasti c a model is proposed, taking advantage of Euler′s elastica and impainting regula rized term. A numerical additive operating splitting (AOS) scheme is us ed to discre tize the image, which overcomes the time step size restriction for explicit sche m e. Experimental results show that the proposed model performs well in simulation, while leaving isolated particles on SA R imag e. To solve the problem, the proposed method is complemented through Gauss filtering in conjunction with the proposed model. Results verify that the pr oposed method can eliminate the large particles effectively and suppress the staircase effect with a high equivalent numbe r of looks (ENL).