The microstructure, martensitic transformation behavior, mechanical and shape memory properties of the Ti–V–Al–Cu light weight shape memory alloys were investigated systematically. The results showed that the phase constitution gradually evolved from single α″ martensite phase to the complete β phase with the Cu content increasing in the solution treated Ti–13V–3Al-xCu alloys at room temperature. The spear-like martensite variant constituted the typical self-accommodation configuration, and {111} type I twins and <211> type II twins coexisted in the Ti–V–Al–Cu alloys. Moreover, Ti2Cu precipitate can be observed in the Ti–V–Al–Cu alloys with the higher Cu contents. The martensitic transformation temperature of Ti–V–Al–Cu alloys decreased continuously with the increased Cu content. The Ti–V–Al–Cu alloys with the higher transformation temperature and higher strength as well as the superior shape recovery characteristics can be obtained by tailoring Cu content. It was the perfect combination of solid solution strengthening, grain refinement and precipitation strengthening to promote the enhancement of matrix strength. The maximum recoverable strain was 4.4%, for 6% pre-strain and the reverse martensite transformation temperature was 334 °C in the optimal Ti–13V–3Al-0.5Cu alloy.