An affine translation surface is a graph of a function   introduced by Liu and Yu in 2013. The article considers the spacelike affine translation surfaces in the Minkowski space  with density  establishing the Lagrange’s equation type for -maximal surface, classifying -maximal spacelike affine translation surfaces. The result obtains two parameters and . From that, the Calabi – Bernstein theorem in this space is not true because two function  and  are defined on