As the model fused a linear model and a nonlinear model is beneficial to digital image filtering, this paper explores a generalized autoregressive model on the basis of Weierstrass theory for image adaptive filtering. The model fuses both linear and nonlinear autoregressive models into a uniform expression and simulation experiments verify that the model can fit both conventional linear and nonlinear autoregressive models well. By using a bi-vector instead of a scalar parameter, the bi-dimensional expression of the model is deduced, then a generalized M-estimator is chosen to estimate parameters by a contrast analysis. The experimental results indicate that the proposed algorithm has a fast convergence speed, the average iterations are no more than 6 times and the computing time for linear model and quadratic model is 150 s and 418 s respectively. Moreover,it can remove image noises while conserve detailed image information effectively.