  In this study, we give weighted mean and weighted Gaussian curvatures of two
types of timelike general rotational surfaces with non-null plane meridian
curves in four-dimensional Minkowski space E^4_1 with density
e^({\lambda}_1x^2+{\lambda}_2^y2+{\lambda}_3z^2+{\lambda}_4t^2), where
{\lambda}_i (i = 1,2,3,4) are not all zero and we give some results about
weighted minimal and weighted flat timelike general rotational surfaces in
E^4_1 with density. Also, we construct some examples for these surfaces.
