Abstract: The canal surfaces with time-like center curves in 3D Minkowski space were defined and the Weingarten canal surfaces were classified. Similar to the studying method for surfaces in Euclidean space， at first， the parametric equation of canal surfaces under pseudo orthogonal frame was built according to the Frenet frame of time-like curves and the geometric definition of canal surfaces， then the basic theories were obtained which include two fundamental quantities， the Gaussian curvature and mean curvature and so on. Using basic theories， the relationship between the Gaussian curvature and the mean curvature were found and the Weingarten canal surfaces were studied explicitly. The conclusion was achieved that a canal surface is a Weingarten surface if and only if it is a tube or a revolution surface.

Key words: Minkowski space, canal surfaces, Weingarten surfaces, Gaussian curvature, mean curvature