  A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a
generalized constant ratio (GCR) hypersurface if the tangential part of its
position vector is one of its principle directions. In this work, we move the
study of generalized constant ratio hypersurfaces started in \cite%
{YuFu2014GCRS} into the Minkowski space. First, we get some geometrical
properties of non-degenerated GCR hypersurfaces in an arbitrary dimensional
Minkowski space. Then, we obtain complete classification of GCR surfaces in the
Minkowski 3-space. We also give some explicit examples.
