Abstract: Special surfaces in the Minkowski space were studied on the basis of the invariant theory and theory of differential equation. Some categories were presented by changing the partial differential equation into the ordinary differential equation to simplify the solving process. Affine translation Weingarten surfaces were studied under the pseudo orthogonal frame. The first and second fundamental forms， Gaussian curvature and mean curvature of the surfaces were obtained according to the basic principles of differential geometry. The classification theorems of those translation surfaces were given mainly by using the linear and square relationships between the Gaussian curvature and the mean curvature.

Key words: Minkowski space, affine translation surface, mean curvature, Gaussian curvature, Weingarten surface