The recent increasing interest of T-phase in Al alloy has been switched to its twins. In this study, we employed high resolution transmission electron microscopy to study and compare the morphology and orientation relationships (OR) of T-phase and its twins in an Al-Cu-Mg-Mn alloy. It is found that T-phase tends to form on the {403}(Al) habit planes and exhibit a rod-like shape, with it longitudinal axis, [010](T), being parallel to the matrix [010](Al) direction. Three different OR types are determined between T-phase and Al matrix, namely, {200}(T)aOE (c) 010 >(T)//{200}(Al)aOE (c) 010 >(Al) (OR-I), {200}(T)aOE (c) 010 >(T)//aOE (c) 010 >(Al) (OR-II), and {200}(T)aOE (c) 010 >(T)//{301}(Al)aOE (c) 010 >(Al) (OR-III). OR-II is the most widely observed OR, while OR-I and III can form from the OR-II by twinning. During the twinning, the cross-section of T-phase transforms from a parallelogram-like shape into a shell-like shape. Further analyses on the shell-like T-twins strongly suggest that tenfold twins could form directly from the successive twinning of an individual T crystal.