The present study investigated the microstructure, phase transformation behavior, and functional characteristics of the multicomponent Ti–Ni–Cu–Al–V shape memory alloys with the different annealing treatments. The results indicated that the multicomponent Ti–Ni–Cu–Al–V alloy annealed at 673 K/5 min was primarily composed of the B2 parent phase and Ti2(Ni,Cu) type precipitates distributing along the grain boundaries. As the annealing temperature increased and the annealing time extended, the chemical composition of the matrix changed slightly due to the precipitation of the Ti2(Ni,Cu) phase. Consequently, the martensitic phase (B19) gradually appeared and the volume friction of the martensite phase gradually increased. The phase constituents of the present Ti–Ni–Cu–Al–V shape memory alloy evolved from a B2 austenite phase to a B19 martensite phase with the annealing temperature/time increasing. Additionally, as the annealing temperature and time increased, the grain size also increased. The increment in annealing temperature and the prolongation of annealing time resulted in an increase of martensitic transformation temperatures as a result of the comprehensive effect of chemical composition, grain size, defects’ density, etc. Both yield strength and fracture strength decreased, while the elongation significantly increased (reaching 28% at 1123 K/60 min) with the annealing temperature rising and annealing time prolonging. Under the successively applied prestrain to 8% condition, the recoverable strain decreased from 4.2% to 1.7% for the annealed Ti–Ni–Cu–Al–V shape memory alloy with the annealing temperature/time increasing.