Partial differential equation (PDE) and Markov random field are two kinds of texture preserving regularized image denoising models. In this paper, the equivalence of them is proved: PDE can be derived to have the form of Markov model. Total variation (TV) is a kind of PDE, the adjacent domain of it is first order. Based on Markov theory, the adjacent domain of TV is enlarged to second order and it can contain more image information; image processed by the new TV-Markov model has little staircasing. In the new model, different coefficient function has different edge preserving property, so the new model is hybrid. Using hybrid functions, the new TV-Markov model has better denoising effect, and it can preserve edge well.