Abstract: While image noise removal methods based on the fourth order partial differential equations show their advantages in producing piecewise smooth results，they are sensitive to the high frequency components in the images and destroy image texture prominently.This paper proposes a texture preserving fourth order partial differential equations based image denoising model.At first，a cost function relying on second derivatives of image intensity function in the direction orthogonal to the gradient is proposed.Then，it proves the existence and uniqueness of this function，and the proposed fourth order partial differential equations are derived from it using gradient descent flow and Euler-Lagrange function in succession.At last，the method is tested on a broad range of real images and demonstrates good noise suppression without destruction of important edges and textures in the image.