Abstract: Discusses the invariants of quadratic surfaces after they rotate around different coordinate axes then translate parallel in the three dimensional Minkowski space. According to these invariants, the equivalent classes of the quadratic surfaces are defined for classification. It is revealed that in the 3D Minkowski space the transformation of quadratic surface includes around both parallel translation and rotation which comprises space-like and time-like axes within orthogonal frame and that around null-like axes within pseudo-orthogonal frame, where different rotation transformation results in different invariants and classification.